The homomorphism \(M^*\otimes N\to Hom(M,N)\)
The author proves the following two results: (i) For two non-zero reflexive modules M and N of finite projective dimensions over a Gorenstein local ring for which Hom(M,N) is a module of syzygies, the natural homomorphism \(M^*\otimes N\to Hom(M,N)\) is an isomorphism. (ii) The projective dimension of a module M over a regular local ring \(R \leq n\Leftrightarrow Ext^ n_ R(M,R)\otimes M\to Ext^ n_ R(M,M)\) is surjective, in which case it is actually bijective. The result extends the usual criterion for the projectivity of a module.
scientific article; zbMATH DE number 3948440
scientific article