平凡扩张上的投射余可解Gorenstein平坦模  

Projectively Coresolved Gorenstein Flat Modules over Trivial Ring Extension

作　　者：王罗唯 WANG Luowei(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《绵阳师范学院学报》2025年第2期1-8,共8页Journal of Mianyang Teachers' College

基　　金：重庆市自然科学基金项目(cstc2018jcyjAX0541);重庆市教委项目(KJQN201800509)。

摘　　要：设R是有单位元的结合环,M是R-R-双模,R■M是平凡扩张.刻画了平凡扩张上的投射余可解Gorenstein平坦模(简称PGF-模):设(X,α)是左(R■M)-模,M作为左R-模和右R-模的投射、平坦维数分别有限,且Ζ(R)=(R,0)是相容(R■M)-(R■M)-双模,则(X,α)是PGF-模当且仅当左R-模Coker(α)是PGF-模且左R-模的序列M■_(R)M■_(R)X→M■_(R)X→X是正合的.Let R■M be the trivial ring extension of R by the R-R-bimodule M where R is an associative ring with identity.This article characterizes projective Gorenstein flat modules (abbreviated as PGF-module) over trivial extensions:Let (X,α) be an (R■M)-module.If pd(_(R)M)<∞,fd(M_(R))<∞,andΖ(R)=(R,0) is a compatible (R■M)-(R■M)-bimodule,then the left (R■M)-module (X,α) is an PGF-module if and only if the left R-module Coker(α) is an PGF-module and the sequence M■_(R)M■_(R)X→M■_(R)X→X is exact.

关 键 词：投射余可解Gorenstein平坦模 平凡扩张 伴随函子 

分 类 号：O154.2[理学—数学]