摘要
本文引入了相关于遗传挠理论的平坦模和 ML 模,利用它们刻划了相关 Coherent环,相关 noether 环以及半遗传环,并使得[3]中主要定理和命题有了更完美的形式,此外,我们还给出了平坦模是τ—平坦模、fg τ—平坦模是投射模的条件。
A left R module M is called τ-flat(τ ML),if for every τf.p.(f.g.)left R module N,any map N→M factors through a f.g.free(τ-f.p.)mod-ule,where τ=(Tτ,Fτ)is an hereditary torsion theory.In this paper,we givesome properties of τ flat and τ ML module,by using them characterize τ c-oherent;τ-noetherian;semihereditary ring,and obtain better form of sometheorems in[3].In addition,we also prove:(1)If R∈Fτ,then left τ-flat m-odule is flat;(2)A f.g.τ flat left R-module M is projective iff Q_τ(R)(?)_RM is projective Q_τ(R)-module,where Q_τ(R) is quotient ring of R.
出处
《数学杂志》
CSCD
北大核心
1992年第2期213-220,共8页
Journal of Mathematics
