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Paper   IPM / M / 16418
School of Mathematics
  Title:   A Study of quasi-Gorenstein rings II: Deformation of quasi-Gorenstein property
  Author(s):  Ehsan Tavanfar (Joint with K. Shimomoto and N. Taniguchi)
  Status:   Published
  Journal: J. Algebra
  Vol.:  562
  Year:  2020
  Pages:   368-389
  Supported by:  IPM
In the present article, we investigate the following deformation problem. Let (R,\fm) be a local (graded local) Noetherian ring with a (homogeneous) regular element y ∈ \fm and assume that R/yR is quasi-Gorenstein. Then is R quasi-Gorenstein? We give positive answers to this problem under various assumptions, while we present a counter-example in general. We emphasize that absence of the Cohen-Macaulay condition requires delicate and subtle studies.

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