In this paper,supersemiprime ring is introduced,relations among the supersemiprime rings and the some rings around it are discussed,supersemiprime radical and its properties are studied.
This short exposition is about some commutativity conditions on a semiprime right Goldie Ck-ring. In particular, it is observed here that a semiprime right Goldie Ck-ring with symmetric quotient is commutative. The st...This short exposition is about some commutativity conditions on a semiprime right Goldie Ck-ring. In particular, it is observed here that a semiprime right Goldie Ck-ring with symmetric quotient is commutative. The statement holds if the symmetric ring is replaced by reduced, 2-primal, left duo, right duo, abelian, NI, NCI, IFP, or Armendariz ring.展开更多
In accordance with the distributive traits of semiprimes’ divisors, the article proposes an approach that can find out the small divisor of a semiprime by parallel computing. The approach incorporates a deterministic...In accordance with the distributive traits of semiprimes’ divisors, the article proposes an approach that can find out the small divisor of a semiprime by parallel computing. The approach incorporates a deterministic search with a probabilistic search, requires less memory and can be implemented on ordinary multicore computers. Experiments show that certain semiprimes of 27 to 46 decimal-bits can be validly factorized with the approach on personal computer in expected time.展开更多
We prove that the multiplication ring of a centrally closed semiprime ring R has a finite rank operator over the extended centroid C iff R contains an idempotent q such that qRq is finitely generated over C and, for e...We prove that the multiplication ring of a centrally closed semiprime ring R has a finite rank operator over the extended centroid C iff R contains an idempotent q such that qRq is finitely generated over C and, for each , there exist and e an idempotent of C such that xz=eq.展开更多
In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Fi...In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.展开更多
Let R be a semiprime ring, R F be its left Martindale quotient ring and I be an essential ideal of R. Then every generalized derivation μ defined on I can be uniquely extended to a generalized derivation of R F . Fur...Let R be a semiprime ring, R F be its left Martindale quotient ring and I be an essential ideal of R. Then every generalized derivation μ defined on I can be uniquely extended to a generalized derivation of R F . Furthermore, if there exists a fixed positive integer n such that μ(x) n = 0 for all x ∈I, then μ = 0.展开更多
Let R be a semiprime ring with the center Z(R), d and g be derivations of R, L be a nonzero left ideal of R and rR(L) = 0. Suppose that d(x)x - xg(x) ∈ Z(R) for all x ∈ L, then d(R) Z(R) and the ideal of R generate...Let R be a semiprime ring with the center Z(R), d and g be derivations of R, L be a nonzero left ideal of R and rR(L) = 0. Suppose that d(x)x - xg(x) ∈ Z(R) for all x ∈ L, then d(R) Z(R) and the ideal of R generated by d(R) is in the center of R.展开更多
Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF...Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF（x）xn＋1-i for all x 6 R. In this case, we prove that F is of the form 2F（x） = D（x） ＋ ax ＋ xa for all x ∈ R, where D ： R → R is a derivation and a 6 R is some fixed element.展开更多
We describe the valued Gabriel quiver of a wedge product of coalgebras and study the category of comodules of a semiprime coalgebra. In particular, we prove that any monomial semiprime k-tame fc-tame coalgebra is stri...We describe the valued Gabriel quiver of a wedge product of coalgebras and study the category of comodules of a semiprime coalgebra. In particular, we prove that any monomial semiprime k-tame fc-tame coalgebra is string. We also prove a version of Eisenbud-Griffith theorem for coalgebras, namely, any hereditary semiprime strictly quasi-finite coalgebra is serial.展开更多
With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of...With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings, and discuss the relationship between strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals and prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings.展开更多
In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean ordered subsemigroups are given by som...In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals of S. Furthermore, some characterizations for an ordered semigroup S to be a chain of archimedean ordered subsemigroups are also given by means of fuzzy subsets of S. In particular, by using the fuzzy prime radical theorem of ordered semigroups, we prove that an ordered semigroup S is a chain of archimedean ordered subsemigroups if and only if S is a semilattice of archimedean ordered subsemigroups and all weakly completely prime fuzzy ideals of S form a chain.展开更多
In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups...In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals. Finally, we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.展开更多
In 1999, Kim and Kwak asked one question that ＂Is a ring R 2-primal if Op C P for each P ∈ mSpec（R）？＇. In this paper, we prove that if Op has the IFP for each P ∈ mSpec（N）, then OR C P for each P ∈ mSpec（N...In 1999, Kim and Kwak asked one question that ＂Is a ring R 2-primal if Op C P for each P ∈ mSpec（R）？＇. In this paper, we prove that if Op has the IFP for each P ∈ mSpec（N）, then OR C P for each P ∈ mSpec（N） if and only if N is a 2-primal near-ring and also we give characterization of 2-primal nearrings by using its minimal O-prime ideals.展开更多
In this paper we characterize those hemirings for which each k-ideal is idempotent. We also characterize those hemirings for which each fuzzy k-ideal is idempotent. The space of prime k-ideals (fuzzy k-prime k-ideals)...In this paper we characterize those hemirings for which each k-ideal is idempotent. We also characterize those hemirings for which each fuzzy k-ideal is idempotent. The space of prime k-ideals (fuzzy k-prime k-ideals) is topologized.展开更多
Based on the knowledge off-algebra, the concept of quotient f-algebra is mainly discussed. The sufficient condition when the quotient space is quotient f-algebra is given, and the quotient f-algebra that makes the ker...Based on the knowledge off-algebra, the concept of quotient f-algebra is mainly discussed. The sufficient condition when the quotient space is quotient f-algebra is given, and the quotient f-algebra that makes the kernel of a Riesz homomorphism as the equivalence class is obtained. Moreover, some important algebraic properties, such as commutative, semiprime and unital are studied, and the relationship between an f-algebra and its quotient space with respect to these properties are discussed in details.展开更多
Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized p...Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.展开更多
This note proves that, if R is a prime ring of characteristic 2 with d a derivation of R and L a noncentral Lie ideal of R such that [d（u）,u]^n is central, for all u ∈ L, then R must satisfy s4, the standard identi...This note proves that, if R is a prime ring of characteristic 2 with d a derivation of R and L a noncentral Lie ideal of R such that [d（u）,u]^n is central, for all u ∈ L, then R must satisfy s4, the standard identity in 4 variables. The case where R is a semiprime ring is also examined by the authors. The results of the note improve Carini and Filippis＇s results.展开更多
The aim of this paper is to define the notions of generalized （m, n）-derivations and generalized （m, n）：Jordan derivations and to prove two theorems involving these map- pings.
In this paper, we describe ∈-derivations in certain graded algebras by their actions on elements satisfying some special conditions. One of the main results is applied to local ∈-derivations on some certain graded a...In this paper, we describe ∈-derivations in certain graded algebras by their actions on elements satisfying some special conditions. One of the main results is applied to local ∈-derivations on some certain graded algebras.展开更多
Recently, basing on a suitable application of Milne-Bhatnagar＇s characterization theorem about matrix inversions, we have found that Warnaar＇s elliptic matrix inversion can be further extended to the following gener...Recently, basing on a suitable application of Milne-Bhatnagar＇s characterization theorem about matrix inversions, we have found that Warnaar＇s elliptic matrix inversion can be further extended to the following general inversion theorem.展开更多
文摘In this paper,supersemiprime ring is introduced,relations among the supersemiprime rings and the some rings around it are discussed,supersemiprime radical and its properties are studied.
文摘This short exposition is about some commutativity conditions on a semiprime right Goldie Ck-ring. In particular, it is observed here that a semiprime right Goldie Ck-ring with symmetric quotient is commutative. The statement holds if the symmetric ring is replaced by reduced, 2-primal, left duo, right duo, abelian, NI, NCI, IFP, or Armendariz ring.
文摘In accordance with the distributive traits of semiprimes’ divisors, the article proposes an approach that can find out the small divisor of a semiprime by parallel computing. The approach incorporates a deterministic search with a probabilistic search, requires less memory and can be implemented on ordinary multicore computers. Experiments show that certain semiprimes of 27 to 46 decimal-bits can be validly factorized with the approach on personal computer in expected time.
文摘We prove that the multiplication ring of a centrally closed semiprime ring R has a finite rank operator over the extended centroid C iff R contains an idempotent q such that qRq is finitely generated over C and, for each , there exist and e an idempotent of C such that xz=eq.
文摘In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.
基金supported by the mathematical Tianyuan research foundationthe post-doctorate research foundation
文摘Let R be a semiprime ring, R F be its left Martindale quotient ring and I be an essential ideal of R. Then every generalized derivation μ defined on I can be uniquely extended to a generalized derivation of R F . Furthermore, if there exists a fixed positive integer n such that μ(x) n = 0 for all x ∈I, then μ = 0.
基金Supported by the National Natural Science Foundation of China(19671035)
文摘Let R be a semiprime ring with the center Z(R), d and g be derivations of R, L be a nonzero left ideal of R and rR(L) = 0. Suppose that d(x)x - xg(x) ∈ Z(R) for all x ∈ L, then d(R) Z(R) and the ideal of R generated by d(R) is in the center of R.
文摘Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF（x）xn＋1-i for all x 6 R. In this case, we prove that F is of the form 2F（x） = D（x） ＋ ax ＋ xa for all x ∈ R, where D ： R → R is a derivation and a 6 R is some fixed element.
文摘We describe the valued Gabriel quiver of a wedge product of coalgebras and study the category of comodules of a semiprime coalgebra. In particular, we prove that any monomial semiprime k-tame fc-tame coalgebra is string. We also prove a version of Eisenbud-Griffith theorem for coalgebras, namely, any hereditary semiprime strictly quasi-finite coalgebra is serial.
基金Supported by the National Natural Science Foundation of China(60875034)the Natural Science Foundation of Education Committee of Hubei Province(D20092901),the Natural Science Foundation of Hubei Province(2009CDB340)
文摘With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings, and discuss the relationship between strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals and prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1096101411271040)+4 种基金the Science and Technology Projects in Guangdong Province(Grant No.2010B010600039)the Guangdong Provincial Natural Science Foundation of China(Grant No.S2011010003681)the Anhui Provincial Excellent Youth Talent Foundation (Grant No.2012SQRL115ZD)the University Natural Science Project of Anhui Province(Grant No.KJ2012B133)the Fuyang Normal College Natural Science Foundation(Grant No.2007LZ01)
文摘In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals of S. Furthermore, some characterizations for an ordered semigroup S to be a chain of archimedean ordered subsemigroups are also given by means of fuzzy subsets of S. In particular, by using the fuzzy prime radical theorem of ordered semigroups, we prove that an ordered semigroup S is a chain of archimedean ordered subsemigroups if and only if S is a semilattice of archimedean ordered subsemigroups and all weakly completely prime fuzzy ideals of S form a chain.
基金Supported by the National Natural Science Foundation of China (Grant No. 10961014)the Science and Technology Projects in Guangdong Province (Grant No. 2010B010600039)+3 种基金the Guangdong Provincial Natural Science Foundation of China (Grant No. S2011010003681)the Anhui Provincial Excellent Youth Talent Foundation (Grant No. 2012SQRL115ZD)the University Natural Science Project of Anhui Province (Grant No. KJ2012B133)the Fuyang Normal College Natural Science Foundation (Grant No. 2007LZ01)
文摘In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals. Finally, we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.
文摘In 1999, Kim and Kwak asked one question that ＂Is a ring R 2-primal if Op C P for each P ∈ mSpec（R）？＇. In this paper, we prove that if Op has the IFP for each P ∈ mSpec（N）, then OR C P for each P ∈ mSpec（N） if and only if N is a 2-primal near-ring and also we give characterization of 2-primal nearrings by using its minimal O-prime ideals.
文摘In this paper we characterize those hemirings for which each k-ideal is idempotent. We also characterize those hemirings for which each fuzzy k-ideal is idempotent. The space of prime k-ideals (fuzzy k-prime k-ideals) is topologized.
基金The Science Research Start-up Foundation for Young Teachers of Southwest Jiaotong University ( No.2008Q074)
文摘Based on the knowledge off-algebra, the concept of quotient f-algebra is mainly discussed. The sufficient condition when the quotient space is quotient f-algebra is given, and the quotient f-algebra that makes the kernel of a Riesz homomorphism as the equivalence class is obtained. Moreover, some important algebraic properties, such as commutative, semiprime and unital are studied, and the relationship between an f-algebra and its quotient space with respect to these properties are discussed in details.
文摘Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.
基金Partially supported by China Postdoctoral Science Foundation
文摘This note proves that, if R is a prime ring of characteristic 2 with d a derivation of R and L a noncentral Lie ideal of R such that [d（u）,u]^n is central, for all u ∈ L, then R must satisfy s4, the standard identity in 4 variables. The case where R is a semiprime ring is also examined by the authors. The results of the note improve Carini and Filippis＇s results.
文摘The aim of this paper is to define the notions of generalized （m, n）-derivations and generalized （m, n）：Jordan derivations and to prove two theorems involving these map- pings.
文摘In this paper, we describe ∈-derivations in certain graded algebras by their actions on elements satisfying some special conditions. One of the main results is applied to local ∈-derivations on some certain graded algebras.
文摘Recently, basing on a suitable application of Milne-Bhatnagar＇s characterization theorem about matrix inversions, we have found that Warnaar＇s elliptic matrix inversion can be further extended to the following general inversion theorem.
