Projectively Coresolved Gorenstein Flat Modules over Trivial Ring Extension
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.
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