Presentations of rings with non-trivial semidualizing modules

Details Presentations of rings with non-trivial semidualizing modules Presentations of rings with non-trivial semidualizing modules

2009-05-05

arxiv.org/abs/0905.0685v2

Mathematics

Commutative Algebra

16 pages, uses XY-pic; v.2 reorganized, main theorem revised, examples added

Scientific paper

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.

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