Let△(φ,ψ)=(ABMA ANBB)be a Morita ring which is an Artin algebra.In this paper we investigate the relations between the Gorenstein-projective modules over a Morita ring△(φ,ψ)and the algebras A and B.We prove that...Let△(φ,ψ)=(ABMA ANBB)be a Morita ring which is an Artin algebra.In this paper we investigate the relations between the Gorenstein-projective modules over a Morita ring△(φ,ψ)and the algebras A and B.We prove that if△(φ,ψ)is a Gorenstein algebra and both Ma and aN(resp.,both NB and BM)have finite projective dimension,then A(resp.,B)is a Gorenstein algebra.We also discuss when the CM-freeness and the CM-finiteness of a Morita ring△(φ,ψ)is inherited by the algebras A and B.展开更多
基金This work was supported by the NNSFC(National Natural Science Foundation of China)Grant No.11971304.
文摘Let△(φ,ψ)=(ABMA ANBB)be a Morita ring which is an Artin algebra.In this paper we investigate the relations between the Gorenstein-projective modules over a Morita ring△(φ,ψ)and the algebras A and B.We prove that if△(φ,ψ)is a Gorenstein algebra and both Ma and aN(resp.,both NB and BM)have finite projective dimension,then A(resp.,B)is a Gorenstein algebra.We also discuss when the CM-freeness and the CM-finiteness of a Morita ring△(φ,ψ)is inherited by the algebras A and B.
