# Presentations of rings with non-trivial semidualizing modules

@article{Jorgensen2009PresentationsOR,
title={Presentations of rings with non-trivial semidualizing modules},
author={David A. Jorgensen and Graham J. Leuschke and Sean Sather-Wagstaff},
journal={Collectanea Mathematica},
year={2009},
volume={63},
pages={165-180}
}
• Published 2009
• Mathematics
• Collectanea Mathematica
Let R be a commutative noetherian local ring. A finitely generated R-module C is semidualizing if it is self-orthogonal and $${{\rm Hom}_R(C,C)\cong R}$$ . 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… Expand
14 Citations
Presentations of rings with a chain of semidualizing modules
• Mathematics
• 2014
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Tate cohomology with respect to semidualizing modules
• Mathematics
• 2009
We investigate Tate cohomology of modules over a commutative noetherian ring with respect to semidualizing modules. We identify classes of modules admitting Tate resolutions and analyze theExpand