This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasi...This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasidiagonal extension.We give also an example of generalized quasidiagonal extension,which is not quasidiagonal extension.展开更多
The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce t...The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.展开更多
In this paper,we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair.We introduce a cohomology theory of 3-LieHDer pairs.Next,we interpret the second cohomology group as the space o...In this paper,we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair.We introduce a cohomology theory of 3-LieHDer pairs.Next,we interpret the second cohomology group as the space of all isomorphism classes of abelian extensions.Finally,we consider formal deformations of 3-LieHDer pairs that are governed by the cohomology with self-coefficient.展开更多
In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of au...In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras.Finally,we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.展开更多
This paper introduce the concept of locally quasidiagonal extension of C^(*)-algebras and give some basic properties.We use the method of analogy,based on some properties possessed by quasidiagonal extensions,we inves...This paper introduce the concept of locally quasidiagonal extension of C^(*)-algebras and give some basic properties.We use the method of analogy,based on some properties possessed by quasidiagonal extensions,we investigate whether local quasidiagonal extensions still retain these properties.We then show that an extension of a locally AF algebra by a locally AF algebra is a locally quasidiagonal extension.展开更多
South China is the most important polymetallic （tungsten, tin, bismuth, copper, silver, antimony, mercury, rare metals, heavy rare earth elements, gold and lead-zinc） province in China. This paper describes the basi...South China is the most important polymetallic （tungsten, tin, bismuth, copper, silver, antimony, mercury, rare metals, heavy rare earth elements, gold and lead-zinc） province in China. This paper describes the basic characteristics of Mesozoic large-scale mineralization in South China. The large-scale mineralization mainly took place in three intervals： 170-150 Ma, 140-126 Ma and 110-80 Ma. Among these the first stage is mainly marked by copper, lead-zinc and tungsten mineralization and the third stage is mainly characterized by tin, gold, silver and uranium mineralization. The stage of 140-126 Ma mainly characterized by tungsten and tin mineralization is a transitional interval from the first to the third stage. In fight of the current research results of the regional tectonic evolution it is proposed that the large-scale mineralization in the three stages is related to post-collision between the South China block and the North China block, transfer of the principal stress-field of tectonic regimes from N-S to E-W direction, and multiple back-arc lithospheric extensions caused by subduction of the Paleo-Pacific plate.展开更多
In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some ...In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.展开更多
By using a simple analytic method the following inequalities are proved:(b x+y -a x+y )/(b x-a x)≥[(x+y)/x][(a+b)/2] y, for 0<a<b,x≥1,y>0,x+y≥2; (b x+y -a x+y )/(b x-a x)<[(x...By using a simple analytic method the following inequalities are proved:(b x+y -a x+y )/(b x-a x)≥[(x+y)/x][(a+b)/2] y, for 0<a<b,x≥1,y>0,x+y≥2; (b x+y -a x+y )/(b x-a x)<[(x+y)/x][(a+b)/2] y, for 0<a<b,0<x<1,y>0,x+y≤2. These inequalities are the extensions of inequalities of Qi Feng, Xu Senlin and Zheng Lin. And a conjection of Qi Feng is proved not true.展开更多
Let R be a ring with an endomorphism α and an α-derivation δ. We introduce the notions of symmetric α-rings and weak symmetric α-rings which are generalizations of symmetric rings and weak symmetric rings, respec...Let R be a ring with an endomorphism α and an α-derivation δ. We introduce the notions of symmetric α-rings and weak symmetric α-rings which are generalizations of symmetric rings and weak symmetric rings, respectively, discuss the relations between symmetric α-rings and related rings and investigate their extensions. We prove that if R is a reduced ring and α（1） = 1, then R is a symmetric α-ring if and only if R[x]/（x^n） is a symmetric q^--ring for any positive integer n. Moreover, it is proven that if R is a right Ore ring, α an automorphism of R and Q（R） the classical right quotient ring of R, then R is a symmetric α-ring if and only if Q（R） is a symmetric α-ring. Among others we also show that if a ring R is weakly 2-primal and （α, δ）-compatible, then R is a weak symmetric α-ring if and only if the Ore extension R[x; α, δ] of R is a weak symmetric α^--ring.展开更多
The aim of this article is to summarize the relationship between double Ore extensions and iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a(right) double Ore extension B of...The aim of this article is to summarize the relationship between double Ore extensions and iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a(right) double Ore extension B of A which can not be presented as iterated Ore extensions.展开更多
A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorph...A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorphism and δ an α- derivation of a ring R. We prove that （1） If R is an （α, δ）-compatible and weakly 2-primal ring, then R[x; α, δ] is weakly semicommutative; （2） If R is （α, δ）-compatible, then R is weakly 2-primal if and only if R[x; α, δ] is weakly 2-primal.展开更多
Let R be a noetherian ring and S an excellent extension of R.cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M.We prove that if M S is a right S-module then cid(M S)=...Let R be a noetherian ring and S an excellent extension of R.cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M.We prove that if M S is a right S-module then cid(M S)=cid(M R) and if S M is a left S-module then cfd(S M)=cfd(R M).Moreover,cid-D(S)=cid-D(R) and cfd-D(S)=cfdD(R).展开更多
In this paper, we consider Lie triple systems with derivations. A pair consisting of a Lie triple system and a distinguished derivation is called a LietsDer pair. We define a cohomology theory for LietsDer pair with c...In this paper, we consider Lie triple systems with derivations. A pair consisting of a Lie triple system and a distinguished derivation is called a LietsDer pair. We define a cohomology theory for LietsDer pair with coefficients in a representation. We study central extensions of a LietsDer pair. In the next, we generalize the formal deformation theory to LietsDer pairs in which we deform both the Lie triple system bracket and the distinguished derivation. It is governed by the cohomology of LietsDer pair with coefficients in itself.展开更多
In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebra...In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebras and equivalence classes of Maurer-Cartan elements in a DGLA. The structure of the Leibniz algebra on the space of fundamental objects is also analyzed.展开更多
The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- reg...The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.展开更多
In order to restrict non-yielding maneuvers of left-turning vehicles,an optimal design of left-lane line extensions is proposed to solve the problem.A field observation was conducted to collect a data set of left-turn...In order to restrict non-yielding maneuvers of left-turning vehicles,an optimal design of left-lane line extensions is proposed to solve the problem.A field observation was conducted to collect a data set of left-turning vehicles at the beginning of a green phase at two similar intersections(one with a permitted phase and the other with a protected phase).The comparative analysis shows no significant difference in the speed distribution using either a permitted phase or a protected phase,but it reveals that a permitted phase can lead to a larger acceleration when the left-turn vehicles pass through the conflict points.Those indicate the existence of non-yielding maneuvers of left-turn vehicles at signalized intersections with a permitted phase.Optimal designed left-lane line extensions contain two types of segments,circular curves and transition curves,and they are only related to four geometry parameters of an intersection.The proposed method is easy to use and it can offer reference for intersection channelization and traffic organization.展开更多
Let_(R)C_(S) be a semidualizing(R,S)-bimodule.Then_(R)C_(S) induces an equivalent between the Auslander class A_(C)(S)and the Bass class B_C(R).Let A and B be free normalizing extensions of R and S respectively.In thi...Let_(R)C_(S) be a semidualizing(R,S)-bimodule.Then_(R)C_(S) induces an equivalent between the Auslander class A_(C)(S)and the Bass class B_C(R).Let A and B be free normalizing extensions of R and S respectively.In this paper,we prove that Hom S(_(B)B_(S),_(R)C_(S))is a semidualizing(A,B)-bimodule under some suitable conditions,and so Hom S(_(B)B_(S),_(R)C_(S))induces an equivalence between the Auslander class AHomS (_(B)B_(S),_(R)C_(S))(B). and the Bass class BHomS (BBS,RCS)(A) Furthermore,under a suitable condition on_(R)C_(S),we develop a generalized Morita theory for Auslander categories.展开更多
In this paper, we study n-Gorenstein projective modules over Frobenius extensions and n-Gorenstein projective dimensions over separable Frobenius extensions. Let R ■ A be a Frobenius extension of rings and M any left...In this paper, we study n-Gorenstein projective modules over Frobenius extensions and n-Gorenstein projective dimensions over separable Frobenius extensions. Let R ■ A be a Frobenius extension of rings and M any left A-module. It is proved that M is an n-Gorenstein projective left A-module if and only if A ■_(R)M and Hom_(R)(A, M) are n-Gorenstein projective left A-modules if and only if M is an n-Gorenstein projective left R-module. Furthermore, when R ■ A is a separable Frobenius extension, n-Gorenstein projective dimensions are considered.展开更多
A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper ...A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.展开更多
基金Supported by NSF of Jiangsu Province(No.BK20171421)。
文摘This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasidiagonal extension.We give also an example of generalized quasidiagonal extension,which is not quasidiagonal extension.
基金National Natural Science Foundation of China(12161013)Research Projects of Guizhou University of Commerce in 2024。
文摘The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the Basic Research Program(Natural Science)of Guizhou Province(Grant No.ZK[2023]025).
文摘In this paper,we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair.We introduce a cohomology theory of 3-LieHDer pairs.Next,we interpret the second cohomology group as the space of all isomorphism classes of abelian extensions.Finally,we consider formal deformations of 3-LieHDer pairs that are governed by the cohomology with self-coefficient.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the School-Level Student Research Project of Guizhou University of Finance and Economics(Grant No.2024ZXSY239).
文摘In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras.Finally,we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.
文摘This paper introduce the concept of locally quasidiagonal extension of C^(*)-algebras and give some basic properties.We use the method of analogy,based on some properties possessed by quasidiagonal extensions,we investigate whether local quasidiagonal extensions still retain these properties.We then show that an extension of a locally AF algebra by a locally AF algebra is a locally quasidiagonal extension.
文摘South China is the most important polymetallic （tungsten, tin, bismuth, copper, silver, antimony, mercury, rare metals, heavy rare earth elements, gold and lead-zinc） province in China. This paper describes the basic characteristics of Mesozoic large-scale mineralization in South China. The large-scale mineralization mainly took place in three intervals： 170-150 Ma, 140-126 Ma and 110-80 Ma. Among these the first stage is mainly marked by copper, lead-zinc and tungsten mineralization and the third stage is mainly characterized by tin, gold, silver and uranium mineralization. The stage of 140-126 Ma mainly characterized by tungsten and tin mineralization is a transitional interval from the first to the third stage. In fight of the current research results of the regional tectonic evolution it is proposed that the large-scale mineralization in the three stages is related to post-collision between the South China block and the North China block, transfer of the principal stress-field of tectonic regimes from N-S to E-W direction, and multiple back-arc lithospheric extensions caused by subduction of the Paleo-Pacific plate.
基金National Natural Science Foundation of China(10271076)
文摘In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.
文摘By using a simple analytic method the following inequalities are proved:(b x+y -a x+y )/(b x-a x)≥[(x+y)/x][(a+b)/2] y, for 0<a<b,x≥1,y>0,x+y≥2; (b x+y -a x+y )/(b x-a x)<[(x+y)/x][(a+b)/2] y, for 0<a<b,0<x<1,y>0,x+y≤2. These inequalities are the extensions of inequalities of Qi Feng, Xu Senlin and Zheng Lin. And a conjection of Qi Feng is proved not true.
基金Supported by the National Natural Science Foundation of China(Grant No.11101217)the Natural Science Foundation of Jiangsu Province(Grant No.BK20141476)
文摘Let R be a ring with an endomorphism α and an α-derivation δ. We introduce the notions of symmetric α-rings and weak symmetric α-rings which are generalizations of symmetric rings and weak symmetric rings, respectively, discuss the relations between symmetric α-rings and related rings and investigate their extensions. We prove that if R is a reduced ring and α（1） = 1, then R is a symmetric α-ring if and only if R[x]/（x^n） is a symmetric q^--ring for any positive integer n. Moreover, it is proven that if R is a right Ore ring, α an automorphism of R and Q（R） the classical right quotient ring of R, then R is a symmetric α-ring if and only if Q（R） is a symmetric α-ring. Among others we also show that if a ring R is weakly 2-primal and （α, δ）-compatible, then R is a weak symmetric α-ring if and only if the Ore extension R[x; α, δ] of R is a weak symmetric α^--ring.
文摘The aim of this article is to summarize the relationship between double Ore extensions and iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a(right) double Ore extension B of A which can not be presented as iterated Ore extensions.
基金The NSF(11071097,11101217)of Chinathe NSF(BK20141476)of Jiangsu Province
文摘A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorphism and δ an α- derivation of a ring R. We prove that （1） If R is an （α, δ）-compatible and weakly 2-primal ring, then R[x; α, δ] is weakly semicommutative; （2） If R is （α, δ）-compatible, then R is weakly 2-primal if and only if R[x; α, δ] is weakly 2-primal.
文摘Let R be a noetherian ring and S an excellent extension of R.cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M.We prove that if M S is a right S-module then cid(M S)=cid(M R) and if S M is a left S-module then cfd(S M)=cfd(R M).Moreover,cid-D(S)=cid-D(R) and cfd-D(S)=cfdD(R).
基金Supported by the National Natural Science Foundation of China (Grant No. 12161013)the General Project of Guizhou University of Finance and Economics (Grant No. 2021KYYB16)。
文摘In this paper, we consider Lie triple systems with derivations. A pair consisting of a Lie triple system and a distinguished derivation is called a LietsDer pair. We define a cohomology theory for LietsDer pair with coefficients in a representation. We study central extensions of a LietsDer pair. In the next, we generalize the formal deformation theory to LietsDer pairs in which we deform both the Lie triple system bracket and the distinguished derivation. It is governed by the cohomology of LietsDer pair with coefficients in itself.
基金Supported by National Natural Science Foundation of China under Grant No.11471139National Natural Science Foundation of Jilin Province under Grant No.20170101050JC
文摘In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebras and equivalence classes of Maurer-Cartan elements in a DGLA. The structure of the Leibniz algebra on the space of fundamental objects is also analyzed.
基金The Foundation for Excellent Doctoral Dissertationof Southeast University (NoYBJJ0507)the National Natural ScienceFoundation of China (No10571026)the Natural Science Foundation ofJiangsu Province (NoBK2005207)
文摘The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.
基金The National Natural Science Foundation of China(No.51278220)
文摘In order to restrict non-yielding maneuvers of left-turning vehicles,an optimal design of left-lane line extensions is proposed to solve the problem.A field observation was conducted to collect a data set of left-turning vehicles at the beginning of a green phase at two similar intersections(one with a permitted phase and the other with a protected phase).The comparative analysis shows no significant difference in the speed distribution using either a permitted phase or a protected phase,but it reveals that a permitted phase can lead to a larger acceleration when the left-turn vehicles pass through the conflict points.Those indicate the existence of non-yielding maneuvers of left-turn vehicles at signalized intersections with a permitted phase.Optimal designed left-lane line extensions contain two types of segments,circular curves and transition curves,and they are only related to four geometry parameters of an intersection.The proposed method is easy to use and it can offer reference for intersection channelization and traffic organization.
基金Supported by the Natural Science Foundation of Anhui Province(Grant No.2008085QA03)。
文摘Let_(R)C_(S) be a semidualizing(R,S)-bimodule.Then_(R)C_(S) induces an equivalent between the Auslander class A_(C)(S)and the Bass class B_C(R).Let A and B be free normalizing extensions of R and S respectively.In this paper,we prove that Hom S(_(B)B_(S),_(R)C_(S))is a semidualizing(A,B)-bimodule under some suitable conditions,and so Hom S(_(B)B_(S),_(R)C_(S))induces an equivalence between the Auslander class AHomS (_(B)B_(S),_(R)C_(S))(B). and the Bass class BHomS (BBS,RCS)(A) Furthermore,under a suitable condition on_(R)C_(S),we develop a generalized Morita theory for Auslander categories.
基金Supported by the National Natural Science Foundation of China (Grant No. 11561061)。
文摘In this paper, we study n-Gorenstein projective modules over Frobenius extensions and n-Gorenstein projective dimensions over separable Frobenius extensions. Let R ■ A be a Frobenius extension of rings and M any left A-module. It is proved that M is an n-Gorenstein projective left A-module if and only if A ■_(R)M and Hom_(R)(A, M) are n-Gorenstein projective left A-modules if and only if M is an n-Gorenstein projective left R-module. Furthermore, when R ■ A is a separable Frobenius extension, n-Gorenstein projective dimensions are considered.
基金The NSF(11471108) of Chinathe NSF(2015JJ2051,2016JJ2050) of Hunan Provincethe Teaching Reform Foundation(G21316) of Hunan Province
文摘A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.
