关于拟平坦模的几个注记

本文所有的环均指有单位元的环,模均指酉模。左R-模M称为拟内射的,如果对任意N

Some Remarks of Quasi-flat Modules

In this paper, we solve Ahsan's problem provided in 3], that is ,whether the characterization of commutative regular ring as each submodule of quasi-flat module is quasi-flat is true in the noncommutative case. In §3, we proved that Th3.1. Let R is commutative ring, then R is regular ring iff every quasi-flat module is flat. As a consequently, if R is commutative ring, then R is regular ring iff R is generalized QI-ring (3,Th.3.11, Th.3.4]); if R is left self-injective ring, then R is regular ring iff every left quasi-injective module is fp-injective.