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 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
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
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
In this paper, we extend the concept of Ako and Ol~ families to submodules, study the behavior of the extended prime submodule principle and use these concepts to give new proofs of some familiar theorems.
引进了子模的w-根的概念,并讨论了它的性质.作为所得结果的应用,分别对乘法模与有限生成自由模上的w-根进行了研究.特别地,证明了若F=R^((n)),N= sum from i=1 to m Rα_i■F,且α∈F,则α∈w-rad_F N当且仅当[α,α_1,…,α_m]_t■w-ra...引进了子模的w-根的概念,并讨论了它的性质.作为所得结果的应用,分别对乘法模与有限生成自由模上的w-根进行了研究.特别地,证明了若F=R^((n)),N= sum from i=1 to m Rα_i■F,且α∈F,则α∈w-rad_F N当且仅当[α,α_1,…,α_m]_t■w-rad_R[0,α_1,…,α_m]_t,其中1≤t≤min{m+1,n}.展开更多
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.
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.
基金Supported by the National Natural Science Foundation of China (10271052) is partially supported by the Specialized Research Fund for the Doctoral Program of China Education Ministry (Grant No. 20030284033).
文摘In this paper, we extend the concept of Ako and Ol~ families to submodules, study the behavior of the extended prime submodule principle and use these concepts to give new proofs of some familiar theorems.
文摘引进了子模的w-根的概念,并讨论了它的性质.作为所得结果的应用,分别对乘法模与有限生成自由模上的w-根进行了研究.特别地,证明了若F=R^((n)),N= sum from i=1 to m Rα_i■F,且α∈F,则α∈w-rad_F N当且仅当[α,α_1,…,α_m]_t■w-rad_R[0,α_1,…,α_m]_t,其中1≤t≤min{m+1,n}.
