关于NA-内射模

On NA-injective Modules

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.