摘要:
设
是Morita环，其中A和B是环，N是(A,B)-双模，M是(B,A)-双模，并且Δ
(φ,ψ)是Artin代数。本文主要研究了Morita环Δ
(φ,ψ)上的Gorenstein内射模与代数A和代数B的关系。给出了函子H
A和函子H
B保持Gorenstein内射模的等价条件。设(X,Y,f,g)是Morita环Δ
(φ,ψ)上的一个Gorenstein内射模，本文也证明了在一定条件下
AX和Y
B也是Gorenstein内射模。
Abstract:
Let
be a Morita ring, where A and B are rings, N is (A,B)-bimodule, M is (B,A)-bimodule, and Δ
(φ,ψ) is an Artin algebra. In this paper we investigate the relations between the Gorenstein injective modules over a Morita ring Δ
(φ,ψ) and algebras A and B. The equivalent conditions for functors H
A and H
B to preserve Gorenstein injective modules are given. Let (X,Y,f,g) be a Gorenstein injective module on Morita ring Δ
(φ,ψ). It is also proved that
AX and Y
B are Gorenstein injective modules under certain conditions.