P-平坦模的特征

Characteristic of P-flat Modules

给出了P-平坦模的定义,然后给出了P-平坦模的一些特征,而后定义了维数lTPD(R),并且研究了这个整体维数。得到了一些重要的结果:(1)每一个P-平坦模的商模是P-平坦的,等价于内射模的商模是P-平坦的;(2)R是左完全环等价于每一个左R-模是P-平坦的。

This paper gives the definition and some properties of P-flat module.The dimension lTPD(R) is defined,and this global dimension is investigated.Some important results are deduced.The followings are equivalent for a ring R:(1)Every quotient module of a P-flat module is P-flat;(2)Every quotient module of an injective module is flat.And the followings are equivalent for a ring R:(1)R is left perfect;(2) Every left R module is flat.