Presentations of rings with non-trivial semidualizing modules

• Autores: David A. Jorgensen, Graham J. Leuschke, Sean Sather-Wagstaff
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 63, Fasc. 2, 2012, págs. 165-180
• Idioma: inglés
• DOI: 10.1007/s13348-010-0024-6
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• Resumen

  • Let R be a commutative noetherian local ring. A finitely generated R-module C is semidualizing if it is self-orthogonal and Hom?(?,?)≅? . We prove that a Cohen–Macaulay ring R with dualizing module D admits a semidualizing module C satisfying ?≆?≆? 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.