Organic-inorganic hybrid metal halide perovskite solar cells(PSCs)have attracted much attention due to their high photoelectric conversion efficiency(PCE)and low cost.The certificated PCE of small active area(below 0....Organic-inorganic hybrid metal halide perovskite solar cells(PSCs)have attracted much attention due to their high photoelectric conversion efficiency(PCE)and low cost.The certificated PCE of small active area(below 0.1 cm^(2))device has reached 26.7%[1].However,when considering the scaled-up commercialization of PSCs,an obvious efficiency drop exists for the translation to large-area perovskite submodules(PSMs)with areas more than 200 cm^(2),thus limiting the practical commercialization[2].The major PCE gap between small area cells and large area modules arises the drop of open-circuit voltage(VOC)and fill factor(FF).Formamidinium lead iodide(FAPbI_(3))is now the mostly widely used and highly efficient perovskite composition.However,the photo-active black α-FAPbI_(3) phase will spontaneously transform into photo-inactive yellowδ-FAPbI_(3) phase at room temperature[3].展开更多
A right module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules.This article considers the closure of h-...A right module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules.This article considers the closure of h-pure-S-high submodules of QTAG-modules.Here,we determine all submodules S of a QTAG-module M such that each closure of h-pure-S-high submodule of M is h-pure-S^(-)-high in M^(-).A few results of this theme give a comparison of some elementary properties of h-pure-S-high and S-high submodules.展开更多
In this article, we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity. We study some basic properties of almost prime ...In this article, we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity. We study some basic properties of almost prime submodules and give some characterizations of them, especially for （finitely generated faithful） multiplication modules.展开更多
The aim of this paper is to study the conditions by which a P-prime sub-module can be expressed as a finite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equiva...The aim of this paper is to study the conditions by which a P-prime sub-module can be expressed as a finite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equivalent conditions for a ring to be a Dedekind domain are given.展开更多
Let H^(2)(D^(2))be the Hardy space over the bidisk D^(2),and let M_(φ)=[(z-φ(w))^(2)]be the submodule generated by(z-φ(w))^(2),whereφ(w)is a function in H∞(w).The related quotient module is denoted by N_(φ)=H^(2...Let H^(2)(D^(2))be the Hardy space over the bidisk D^(2),and let M_(φ)=[(z-φ(w))^(2)]be the submodule generated by(z-φ(w))^(2),whereφ(w)is a function in H∞(w).The related quotient module is denoted by N_(φ)=H^(2)(D^(2))ΘM_(φ).In the present paper,we study the Fredholmness of compression operators S_(z),S_(w) on N_(φ).Whenφ(w)is a nonconstant inner function,we prove that the Beurling type theorem holds for the fringe operator F_(w) on[(z-w)^(2)]Θz[(z-w)^(2)]and the Beurling type theorem holds for the fringe operator Fz on M_(φ)ΘwM_(φ)ifφ(0)=0.Lastly,we study some properties of F_(w) on[(z-w^(2))^(2)]Θz[(z-w^(2))^(2)].展开更多
In this paper,the authors construct a φ-group for n submodules,which generalizes the classical K-theory and gives more information than the classical ones.This theory is related to the classification theory for indec...In this paper,the authors construct a φ-group for n submodules,which generalizes the classical K-theory and gives more information than the classical ones.This theory is related to the classification theory for indecomposable systems of n subspaces.展开更多
This paper is a brief and selective survey on classification of Hardy Submodules over the polydisk. The survey reports some progress in classification of Hardy submodules
In this paper, some characterizations of prime submodules in flat modules and, particularly, in free modules are given. Furthermore, the height of prime submodules and some saturated chain of prime submodules are also...In this paper, some characterizations of prime submodules in flat modules and, particularly, in free modules are given. Furthermore, the height of prime submodules and some saturated chain of prime submodules are also given.展开更多
Let M be a non-zero module over an associative （not necessarily commutative） ring. In this paper, we investigate the so-called second and coprime submodules of M. Moreover, we topologize the spectrum Spec-s（M） of ...Let M be a non-zero module over an associative （not necessarily commutative） ring. In this paper, we investigate the so-called second and coprime submodules of M. Moreover, we topologize the spectrum Spec-s（M） of second submodules of M and the spectrum Spec-c（M） of coprime submodules of M, study several properties of these spaces and investigate their internlay with the algebraic properties of M.展开更多
On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and ...On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic （S, T）-fuzzy Hv-submodules and interval valued intuitionistic （S, T）-fuzzy submodules are discussed.展开更多
In this paper, we study modules having only finitely many submodules over any ring which is not necessarily commutative. We try to understand how such a module decomposes as a direct sum. We justify that any module V ...In this paper, we study modules having only finitely many submodules over any ring which is not necessarily commutative. We try to understand how such a module decomposes as a direct sum. We justify that any module V having only finitely many submodules over any ring A is an extension of a cyclic A-module by a finite A-module. Under some assumptions on A, such as commutativity of A, we prove that an A-module V has finitely many submodules if and only if V can be written as a direct sum of a cyclic A-module having only finitely many A-submodules and a finite A-module.展开更多
Using the technique of annihilators, we characterize the w^＊-closure of the finite-partition submodule R（N, ～） of a weakly closed nest algebra module U completely; and by virtue of this characterization, we obtain...Using the technique of annihilators, we characterize the w^＊-closure of the finite-partition submodule R（N, ～） of a weakly closed nest algebra module U completely; and by virtue of this characterization, we obtain a sufficient and necessary condition for U to have a maximal w^＊-closed submodule.展开更多
A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schm...A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem.This paper proves that every finitely generated submodule M containing(z)-Φ(w)is Hilbert-Schmidt,where 0(z),p(w)are two finite Blaschke products.展开更多
In the present paper, the author shows that if a homogeneous submodule M of the Bergman module L_a^2(B_d) satisfies P_M-sum from i to ( M_(zi)P_MM*_(zi))≤c/(N + 1)P_M for some number c > 0, then there is a sequenc...In the present paper, the author shows that if a homogeneous submodule M of the Bergman module L_a^2(B_d) satisfies P_M-sum from i to ( M_(zi)P_MM*_(zi))≤c/(N + 1)P_M for some number c > 0, then there is a sequence {f_j } of multipliers and a positive number c such that c'P_M ≤sum from j to ( M_(fj)M*_(fj))≤ P_M, i.e., M is approximately representable. The author also proves that approximately representable homogeneous submodules are p-essentially normal for p > d.展开更多
Let R be an associated ring with identity. A new equivalent characterization of pure projective left R-modules is given by applying homological methods. It is proved that a left R-module P is pure projective if and on...Let R be an associated ring with identity. A new equivalent characterization of pure projective left R-modules is given by applying homological methods. It is proved that a left R-module P is pure projective if and only if for any pure epimorphism E→M→0, where E is pure injective, HomR（P, E）→HomR（P, M）→0 is exact. Also, we obtain a dual result of pure injective left R-modules. Furthermore, it is shown that every pure projective left R-module is closed under pure submodule if and only if every pure injective left R-module is closed under pure epimorphic image.展开更多
A module M is called closed weak supplemented if for any closed submodule N of M, there is a submodule K of M such that M=K+N and K∩N<<M. Any direct summand of closed weak supplemented module is also closed wea...A module M is called closed weak supplemented if for any closed submodule N of M, there is a submodule K of M such that M=K+N and K∩N<<M. Any direct summand of closed weak supplemented module is also closed weak supplemented. Any nonsingular image of closed weak supplemented module is closed weak supplemented. Nonsingular V-rings in which all nonsingular modules are closed weak supplemented are characterized in Section 4.展开更多
For a hereditary torsion theory τ, this paper mainly discuss properties of A-τ-injective modules, where A is a fixed left R-module. It is proved that if M is an A-τ-injective, B is a submodule of A, then 1） M is A...For a hereditary torsion theory τ, this paper mainly discuss properties of A-τ-injective modules, where A is a fixed left R-module. It is proved that if M is an A-τ-injective, B is a submodule of A, then 1） M is A/B-τ-injective; 2） M is B-τ-injective when B is τ-dense in A. Furthermore, we show that if A1,A2,... An, are relatively injective modules, then A1 A2 ... An is self-τ-injective if and only if A1 is self-τ-injective for each i.展开更多
In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to character...In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to characterize the primary radical of a finitely generated submodule of a free module.展开更多
Let R be a commutative ring with 1, and M is a (left) R-module. We introduce the concept of coprimarily packed submodules as a proper submodule N of an R-module M which is said to be Coprimarily Packed Submodule. If w...Let R be a commutative ring with 1, and M is a (left) R-module. We introduce the concept of coprimarily packed submodules as a proper submodule N of an R-module M which is said to be Coprimarily Packed Submodule. If where Na is a primary submodule of M for each , then for some . When there exists such that;N is called Strongly Coprimarily Packed submodule. In this paper, we list some basic properties of this concept. We end this paper by explaining the relations between p-compactly packed and coprimarily packed submodules, and also the relations between strongly p-compactly packed and strongly coprimarily packed submodules.展开更多
In this paper, we are interested in the following general question： Given a module Mwhich has finite hollow dimension and which has a finite collection of submodules Ki （ 1≤i≤n） such that M=K1 ＋... ＋Kn can we f...In this paper, we are interested in the following general question： Given a module Mwhich has finite hollow dimension and which has a finite collection of submodules Ki （ 1≤i≤n） such that M=K1 ＋... ＋Kn can we find an expression for the hollow dimension of Min terms of hollow dimensions of modules built up in some way from Kt… ,Kn？ We prove the following theorem： Let Mbe an amply supplemented module having finite hollow dimension and let Ki （ 1 ≤i≤n） be a finite collection of submodules of M such that M=K1 ＋... ＋Kn. Then the hollow dimension h（M） of M is the sum of the hollow dimensions of Ki （1≤i≤n） if and only if Ki is a supplement of K1＋...＋K（i-1）＋K（i＋1）＋...＋Kn in M for each 1≤i≤n.展开更多
基金support from open fund of Fujian Provincial Key Laboratory of Functional Materials and Applications(Xiamen University of Technology,fma2024003)the National Key R&D Program of China(No.2021YFB3500400)the National Natural Science Foundation of China(Nos.52073286 and 22275185).
文摘Organic-inorganic hybrid metal halide perovskite solar cells(PSCs)have attracted much attention due to their high photoelectric conversion efficiency(PCE)and low cost.The certificated PCE of small active area(below 0.1 cm^(2))device has reached 26.7%[1].However,when considering the scaled-up commercialization of PSCs,an obvious efficiency drop exists for the translation to large-area perovskite submodules(PSMs)with areas more than 200 cm^(2),thus limiting the practical commercialization[2].The major PCE gap between small area cells and large area modules arises the drop of open-circuit voltage(VOC)and fill factor(FF).Formamidinium lead iodide(FAPbI_(3))is now the mostly widely used and highly efficient perovskite composition.However,the photo-active black α-FAPbI_(3) phase will spontaneously transform into photo-inactive yellowδ-FAPbI_(3) phase at room temperature[3].
文摘A right module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules.This article considers the closure of h-pure-S-high submodules of QTAG-modules.Here,we determine all submodules S of a QTAG-module M such that each closure of h-pure-S-high submodule of M is h-pure-S^(-)-high in M^(-).A few results of this theme give a comparison of some elementary properties of h-pure-S-high and S-high submodules.
文摘In this article, we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity. We study some basic properties of almost prime submodules and give some characterizations of them, especially for （finitely generated faithful） multiplication modules.
文摘The aim of this paper is to study the conditions by which a P-prime sub-module can be expressed as a finite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equivalent conditions for a ring to be a Dedekind domain are given.
文摘Let H^(2)(D^(2))be the Hardy space over the bidisk D^(2),and let M_(φ)=[(z-φ(w))^(2)]be the submodule generated by(z-φ(w))^(2),whereφ(w)is a function in H∞(w).The related quotient module is denoted by N_(φ)=H^(2)(D^(2))ΘM_(φ).In the present paper,we study the Fredholmness of compression operators S_(z),S_(w) on N_(φ).Whenφ(w)is a nonconstant inner function,we prove that the Beurling type theorem holds for the fringe operator F_(w) on[(z-w)^(2)]Θz[(z-w)^(2)]and the Beurling type theorem holds for the fringe operator Fz on M_(φ)ΘwM_(φ)ifφ(0)=0.Lastly,we study some properties of F_(w) on[(z-w^(2))^(2)]Θz[(z-w^(2))^(2)].
基金Project supported by the National Natural Science Foundation of China(Nos.11231002,10971023)the Shanghai Natural Science Foundation(No.09ZR1402000)
文摘In this paper,the authors construct a φ-group for n submodules,which generalizes the classical K-theory and gives more information than the classical ones.This theory is related to the classification theory for indecomposable systems of n subspaces.
文摘This paper is a brief and selective survey on classification of Hardy Submodules over the polydisk. The survey reports some progress in classification of Hardy submodules
文摘In this paper, some characterizations of prime submodules in flat modules and, particularly, in free modules are given. Furthermore, the height of prime submodules and some saturated chain of prime submodules are also given.
文摘Let M be a non-zero module over an associative （not necessarily commutative） ring. In this paper, we investigate the so-called second and coprime submodules of M. Moreover, we topologize the spectrum Spec-s（M） of second submodules of M and the spectrum Spec-c（M） of coprime submodules of M, study several properties of these spaces and investigate their internlay with the algebraic properties of M.
基金the National Natural Science Foundation of China(60474022)the Key Science Foundation of Education Committee of Hubei Province,China(2004Z002D200529001)
文摘On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic （S, T）-fuzzy Hv-submodules and interval valued intuitionistic （S, T）-fuzzy submodules are discussed.
文摘In this paper, we study modules having only finitely many submodules over any ring which is not necessarily commutative. We try to understand how such a module decomposes as a direct sum. We justify that any module V having only finitely many submodules over any ring A is an extension of a cyclic A-module by a finite A-module. Under some assumptions on A, such as commutativity of A, we prove that an A-module V has finitely many submodules if and only if V can be written as a direct sum of a cyclic A-module having only finitely many A-submodules and a finite A-module.
基金Project partially supported by the National Natural Science Foundation of China(No.10401030)the Zhejiang Natural Science Foundation(No.M103044)
文摘Using the technique of annihilators, we characterize the w^＊-closure of the finite-partition submodule R（N, ～） of a weakly closed nest algebra module U completely; and by virtue of this characterization, we obtain a sufficient and necessary condition for U to have a maximal w^＊-closed submodule.
基金supported by the National Nature Science Foundation of China (Grant Nos.12031002,11971086)supported by the Dalian High-Level Talent Innovation Project (Grant No.2020RD09).
文摘A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem.This paper proves that every finitely generated submodule M containing(z)-Φ(w)is Hilbert-Schmidt,where 0(z),p(w)are two finite Blaschke products.
基金supported by the National Natural Science Foundation of China(Nos.11271075,11371096)Shandong Province Natural Science Foundation(No.ZR2014AQ009)the Fundamental Research Funds of Shandong University(No.2015GN017)
文摘In the present paper, the author shows that if a homogeneous submodule M of the Bergman module L_a^2(B_d) satisfies P_M-sum from i to ( M_(zi)P_MM*_(zi))≤c/(N + 1)P_M for some number c > 0, then there is a sequence {f_j } of multipliers and a positive number c such that c'P_M ≤sum from j to ( M_(fj)M*_(fj))≤ P_M, i.e., M is approximately representable. The author also proves that approximately representable homogeneous submodules are p-essentially normal for p > d.
文摘Let R be an associated ring with identity. A new equivalent characterization of pure projective left R-modules is given by applying homological methods. It is proved that a left R-module P is pure projective if and only if for any pure epimorphism E→M→0, where E is pure injective, HomR（P, E）→HomR（P, M）→0 is exact. Also, we obtain a dual result of pure injective left R-modules. Furthermore, it is shown that every pure projective left R-module is closed under pure submodule if and only if every pure injective left R-module is closed under pure epimorphic image.
基金Project (No. 102028) supported by the Natural Science Foundation of Zhejiang Province, China
文摘A module M is called closed weak supplemented if for any closed submodule N of M, there is a submodule K of M such that M=K+N and K∩N<<M. Any direct summand of closed weak supplemented module is also closed weak supplemented. Any nonsingular image of closed weak supplemented module is closed weak supplemented. Nonsingular V-rings in which all nonsingular modules are closed weak supplemented are characterized in Section 4.
基金Supported by the National Natural Science Foundation of China(10571026)Supported by the Research Foundation of the Education Committee of Anhui Province(2006kj050c)Supported by the Doctoral Foundation of Anhui Normal University
文摘For a hereditary torsion theory τ, this paper mainly discuss properties of A-τ-injective modules, where A is a fixed left R-module. It is proved that if M is an A-τ-injective, B is a submodule of A, then 1） M is A/B-τ-injective; 2） M is B-τ-injective when B is τ-dense in A. Furthermore, we show that if A1,A2,... An, are relatively injective modules, then A1 A2 ... An is self-τ-injective if and only if A1 is self-τ-injective for each i.
文摘In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to characterize the primary radical of a finitely generated submodule of a free module.
文摘Let R be a commutative ring with 1, and M is a (left) R-module. We introduce the concept of coprimarily packed submodules as a proper submodule N of an R-module M which is said to be Coprimarily Packed Submodule. If where Na is a primary submodule of M for each , then for some . When there exists such that;N is called Strongly Coprimarily Packed submodule. In this paper, we list some basic properties of this concept. We end this paper by explaining the relations between p-compactly packed and coprimarily packed submodules, and also the relations between strongly p-compactly packed and strongly coprimarily packed submodules.
文摘In this paper, we are interested in the following general question： Given a module Mwhich has finite hollow dimension and which has a finite collection of submodules Ki （ 1≤i≤n） such that M=K1 ＋... ＋Kn can we find an expression for the hollow dimension of Min terms of hollow dimensions of modules built up in some way from Kt… ,Kn？ We prove the following theorem： Let Mbe an amply supplemented module having finite hollow dimension and let Ki （ 1 ≤i≤n） be a finite collection of submodules of M such that M=K1 ＋... ＋Kn. Then the hollow dimension h（M） of M is the sum of the hollow dimensions of Ki （1≤i≤n） if and only if Ki is a supplement of K1＋...＋K（i-1）＋K（i＋1）＋...＋Kn in M for each 1≤i≤n.
