弱wakamatsu余倾斜模的若干注记

Some notes of weak wakamatsu cotilting modules

利用代数表示论和同调代数的方法,给出了弱wakamatsu余倾斜模的若干等价刻画。证明了C是弱wakamatsu余倾斜模,当且仅当C是Π-self-orthogonal模且每个内射模E均是GC-内射模,当且仅当C是Π-self-orthogonal模且每个内射余生成子是GC-内射模。同时还证明了n-余倾斜模一定是弱wakamatsu余倾斜模。

Using methods of Algebra representation theories and homological algebra,some equivalent characterizations of weak wakamatsu cotilting modules are given.It is proved that C is a weak wakamatsu cotilting module,if and only if C is a Π-self-orthogonal module and E is GC-injective module for every injectve module E,if and only if C is a Π-self-orthogonal module and every injectve cogenerator is GC-injective module.And it is also proved that n-cotilting modules are weak wakamatsu cotilting modules.