David A. Jorgensen, Graham J. Leuschke and Sean Sather-Wagstaff
Abstract: Let R be a commutative noetherian local ring. A finitely generated R-module C is semidualizing if it is self-orthogonal and HomR(C,C) is isomorphic to R. We prove that a Cohen–Macaulay ring R with dualizing module D admits a semidualizing module C satisfying [R not isomorphic to C, C not isomorphic to D] if and only if it is a homomorphic image of a Gorenstein ring in which the defining ideal decomposes in a cohomologically independent way. This expands on a well-known result of Foxby, Reiten and Sharp saying that R admits a dualizing module if and only if R is Cohen–Macaulay and a homomorphic image of a local Gorenstein ring.
Journal: Collectanea Mathematica
URL: http://dx.doi.org/10.1007/s13348-010-0024-6