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
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
设R是有单位元的交换环,M是R-模,如果对M的任意子模N,存在R的理想I,使得N=I·M,则称M是乘法R-模,本文主要结论是:设M=Rx_1+…+Rx_(?),其中x_i=(a_(1i),a_(2i),…,a_(?))∈R^(1×n),i=1,2,…,n,并且sum from i=1 to (?)a_(ii)=1...设R是有单位元的交换环,M是R-模,如果对M的任意子模N,存在R的理想I,使得N=I·M,则称M是乘法R-模,本文主要结论是:设M=Rx_1+…+Rx_(?),其中x_i=(a_(1i),a_(2i),…,a_(?))∈R^(1×n),i=1,2,…,n,并且sum from i=1 to (?)a_(ii)=1,那么当R是下列环之一时:(1)整环;(2)半局部环;(3) J(R)=0,有:M是乘法R-模当且仅当F_2(A)=0,其中F_2(A)表示矩阵A=(a_(ij)_(?)中一切2阶子式在R中生成的理想。展开更多
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}.
文摘设R是有单位元的交换环,M是R-模,如果对M的任意子模N,存在R的理想I,使得N=I·M,则称M是乘法R-模,本文主要结论是:设M=Rx_1+…+Rx_(?),其中x_i=(a_(1i),a_(2i),…,a_(?))∈R^(1×n),i=1,2,…,n,并且sum from i=1 to (?)a_(ii)=1,那么当R是下列环之一时:(1)整环;(2)半局部环;(3) J(R)=0,有:M是乘法R-模当且仅当F_2(A)=0,其中F_2(A)表示矩阵A=(a_(ij)_(?)中一切2阶子式在R中生成的理想。
