Contracting endomorphisms and Gorenstein modules

摘要

A finite module M over a noetherian local ring R is said to be Gorenstein if Ext~i (k, M) = 0 for all i dim R. An endomorphism cp : R -< R of rings is called contracting if p~i (m) C m~2 for some i _> 1. Letting `°R denote the R-module R with action induced by c,o, we prove A finite R-module M is Goreristein if and only if НomR(`PR, M) = M and Extk_R~i(R, M) = 0 for 1 < i < depth R.