#### Document Type

Article

#### Date

11-23-2009

#### Embargo Period

11-15-2011

#### Disciplines

Mathematics

#### Description/Abstract

Let R be a commutative noetherian local ring. A finitely generated R-module C is semidualizing if it is self-orthogonal and satisfies the condition Hom_{R}(C,C) \cong R. We prove that a Cohen-Macaulay ring R with dualizing module D admits a semidualizing module C satisfying R\ncong C \ncong 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.

#### Recommended Citation

Jorgensen, David A.; Leuschke, Graham J.; and Sather-Wagstaff, Sean, "Presentations of Rings with Non-Trivial Semidualizing Modules" (2009). *Mathematics Faculty Scholarship.* Paper 36.

http://surface.syr.edu/mat/36

#### Source

Harvested from arXiv.org

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.

## Additional Information

This manuscript is from arXiv.org, for more information look at http://arxiv.org/abs/0905.0685