非诣零凝聚环

Non-nil Coherent Rings

基于模理论角度给出了非诣零凝聚环的等价刻画。具体地,证明了ɸ-环R是非诣零凝聚环当且仅当ɸ-余平坦模类关于直向极限封闭,当且仅当ɸ-余平坦模类是(预)盖类,当且仅当ɸ-余平坦模的对偶模是ɸ-平坦模。

This paper gives some descriptions of non-nil coherent rings based on module theory.In detail,we show that a ɸ-ring R is non-nil coherent,if and only if the direct limit of ɸ-coflat modules is ɸ-coflat,if and only if the class of ɸ-coflat modules is(pre)covering,if and only if the dual of ɸ-coflat modules is ɸ-flat.