2009/05/05 by David A. Jorgensen, Graham Leuschke, Graham J. Leuschke +4
Mathematics · #13C05 #13D07 #13H10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13C05 #msc:13D07 #msc:13H10
paper · pdf · doi:10.48550/arxiv.0905.0685
16 pages, uses XY-pic; v.2 reorganized, main theorem revised, examples added
openalex publication_date 2009/05/05 · arxiv created 2009/11/23 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 HomR(C,C) ≅ 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.