关于NA-内射模  

On NA-injective Modules

作　　者：班秀和[1] 韦儒和[1] 

机构地区：[1]广西师范学院数学与统计科学学院,广西南宁530001

出　　处：《西北民族大学学报（自然科学版）》2016年第4期5-7,共3页Journal of Northwest Minzu University(Natural Science)

基　　金：国家自然科学基金项目(11461010);广西科技开发项目(1599005-2-13);广西教育厅科研基金项目(KY2015ZD075)

摘　　要：文章中引入了NA-内射模的概念:称M为NA-内射模.如果对于任意模A的任意Noether子模B有B到模M的任意同态均可提升为A到M的同态.文中给出了NA-内射模的等价条件,得到了关于NA-内射模的直积、直和等运算的若干结果,指出了NA-内射模是内射模的实质性推广,运用NA-内射模刻画了Noether环和一类V-环.The concept of NA-injective modules was introduced which was a generalization of injective module in this paper. Let B to be any Noetherian submodule of a right R-module A, M was called a NA-injective module if any homomorphism of B into M extends to one of A into M. Characterizations of NA-injective modules were given, some results concerning the direct products and the direct sums of NA-injective modules are obtained, a NA-injective module which is not injective is given. Noetheri- an rings, a class of V-rings, are characterized by NA-injective modules.

关 键 词：NA-内射模 NOETHER环 V-环 

分 类 号：O153.3[理学—数学]