关于所有子模是纯子模的平坦模(英文)

Flat Module of Which Every Submodule is Pure

引进了一新模类-完全平坦模(每一个商模平坦).并得到了:令M是平坦左R-模,RM是完全平坦模当且仅当RM的所有子模是纯的当且仅当每一个右R-模A是M-平坦的.同时本文用完全平坦模刻画了V.N.正则环.

In this paper, we introduce the completely flat module class. A htf R-module M is called completely flat module if every factor module of M is flat. Let M is a flat left R-module, we get that gM is a completely flat module iff aU suhmodules of gM are pure or erery fight R-module A is Mflat. It is proven that a ring R is V.N. regular iff every factor module of the injeetive R-module is flat.