平凡扩张上的投射余可解Gorenstein平坦模
Projectively Coresolved Gorenstein Flat Modules over Trivial Ring Extension
王罗唯1
作者信息
- 1. 重庆师范大学数学科学学院,重庆 401331
- 折叠
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 ⊗ RM ⊗ RX → M ⊗ RX → X是正合的.
Abstract
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(RM)<∞,fd(MR)<∞,and Ζ(R)=(R,0)is a compat-ible(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 ⊗ RM ⊗ RX → M ⊗ RX → X is exact.
关键词
投射余可解Gorenstein平坦模/平凡扩张/伴随函子Key words
projectively coresolved Gorenstein flat modules/trivial extension/adjoint functor引用本文复制引用
出版年
2025
NETL
NSTL
万方数据