In this paper ， we obtain that, if G is either a basic classical Lie superalgebra of I type or G= B(0, n), every Verma module over G has a unique minimal submodule, And this fails for G=F(4).
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
In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the con...In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.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
The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have ...The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have some bearings on reality,then two major problems immediately arise,viz.real situations are not usually crisp and deterministic;complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously,process and understand.Conventional mathematical tools which require all inferences to be exact,are not always efficient to handle imprecisions in a wide variety of practical situations.Following the latter development,a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications.In this paper,new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed.Regarding novelty and generality,the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples.It is observed that our principal results subsume and refine some important ones in the corresponding domains.As an application,one of our results is utilized to discussmore general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19.展开更多
在文 [7]中 ,史福贵借助于 L - fuzzy关系引入了 L - fuzzy集间的 L - fuzzy映射的概念并借助于其水平截集给出了它的一些等价刻画但没有给出一个 L - fuzzy集的像与逆像的表示。本文的目的就是给出一个 L - fuzzy集的像与逆像的各种等...在文 [7]中 ,史福贵借助于 L - fuzzy关系引入了 L - fuzzy集间的 L - fuzzy映射的概念并借助于其水平截集给出了它的一些等价刻画但没有给出一个 L - fuzzy集的像与逆像的表示。本文的目的就是给出一个 L - fuzzy集的像与逆像的各种等价表示并给出了它们在 L - fuzzy代数中的几个简单应用。展开更多
在文献 [6]中 ,史福贵借助于 L -fuzzy关系定义了 L -fuzzy集间的 L -fuzzy映射并借助于它们的水平截集给出了其若干刻画。在这篇文章中 ,我们将借助于另外的截集给出 L -fuzzy映射的一种新刻画。从而我们也得到了 L -fuzzy单射和 L -fu...在文献 [6]中 ,史福贵借助于 L -fuzzy关系定义了 L -fuzzy集间的 L -fuzzy映射并借助于它们的水平截集给出了其若干刻画。在这篇文章中 ,我们将借助于另外的截集给出 L -fuzzy映射的一种新刻画。从而我们也得到了 L -fuzzy单射和 L -fuzzy满射的新刻画。展开更多
文摘In this paper ， we obtain that, if G is either a basic classical Lie superalgebra of I type or G= B(0, n), every Verma module over G has a unique minimal submodule, And this fails for G=F(4).
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.
基金Supported by the National Natural Science Foundation of China (61175055)the Innovation Term of Higher Education of Hubei Province,China (T201109)+1 种基金the Natural Science Foundation of Hubei Province (2012FFB01101)the Natural Science Foundation of Education Committee of Hubei Province (D20131903)
文摘In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.
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.
基金The Deanship of Scientific Research(DSR)at King Abdulaziz University(KAU),Jeddah,Saudi Arabia has funded this project under Grant Number(G:220-247-1443).
文摘The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have some bearings on reality,then two major problems immediately arise,viz.real situations are not usually crisp and deterministic;complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously,process and understand.Conventional mathematical tools which require all inferences to be exact,are not always efficient to handle imprecisions in a wide variety of practical situations.Following the latter development,a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications.In this paper,new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed.Regarding novelty and generality,the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples.It is observed that our principal results subsume and refine some important ones in the corresponding domains.As an application,one of our results is utilized to discussmore general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19.
文摘在文 [7]中 ,史福贵借助于 L - fuzzy关系引入了 L - fuzzy集间的 L - fuzzy映射的概念并借助于其水平截集给出了它的一些等价刻画但没有给出一个 L - fuzzy集的像与逆像的表示。本文的目的就是给出一个 L - fuzzy集的像与逆像的各种等价表示并给出了它们在 L - fuzzy代数中的几个简单应用。
