Joint work with David A. Jorgensen and Sean Sather-Wagstaff.

**Download Paper** (published version)

**Abstract:**

A result of Foxby, Reiten and Sharp says that a commutative noetherian local ring R admits a dualizing module if and only if R is Cohen–Macaulay and a homomorphic image of a local Gorenstein ring Q. We establish an analogous result by showing that such a ring R having a dualizing module admits a non-trivial finitely generated self-orthogonal module C satisfying Hom_R(C,C) \cong R if and only if R is the homomorphic image of a Gorenstein ring in which the defining ideal decomposes in a non-trivial way, forcing significant structural requirements on the ring R.

**Notes:**

We started working this out at the conference for Mel Hochster in Ann Arbor in 2008. I think the paper contains a very satisfying answer to a natural question. It’s a bit technical, but still quite pretty in my opinion.

**BibTeX code:**

@article {MR2909823, AUTHOR = {Jorgensen, David A. and Leuschke, Graham J. and Sather-Wagstaff, Sean}, TITLE = {Presentations of rings with non-trivial semidualizing modules}, JOURNAL = {Collect. Math.}, FJOURNAL = {Collectanea Mathematica}, VOLUME = {63}, YEAR = {2012}, NUMBER = {2}, PAGES = {165--180}, ISSN = {0010-0757}, MRCLASS = {13D07 (13H10)}, MRNUMBER = {2909823}, MRREVIEWER = {Lars Winther Christensen}, DOI = {10.1007/s13348-010-0024-6}, URL = {http://dx.doi.org/10.1007/s13348-010-0024-6}, }