2025/01/23 by Tony J. Puthenpurakal, Puthenpurakal, Tony J. · 1 citation
Mathematics · #Rings, Modules, and Algebras #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2501.13526
Let (A,\mathfrakm) be a complete Cohen-Macaulay local ring. Assume A is not Gorenstein. We say A is a Teter ring if there exists a complete Gorenstein ring (B,\mathfrakn) with dim B = dim A and a surjective map B → A with e(B) - e(A) = 1 (here e(A) denotes multiplicity of A). We give an intrinsic characterization of Teter rings which are domains. We say a Teter ring is a strongly Teter ring if G(B) = \bigoplusi ≥ 0\mathfrakni/\mathfrakni+1 is also a Gorenstein ring. We give an intrinsic characterizations of strongly Teter rings which are domains. If k is algebraically closed field of characteristic zero and R is a standard graded Cohen-Macaulay k-algebra of finite representation type (and not Gorenstein) then we show that \widehatR_\mathfrakM is a Teter ring (here \mathfrakM is the maximal homogeneous ideal of R).