WEEKLY ACTIVITIES

Presentations of rings with a chain of semidualizing modules
Speaker: Ensiyeh Amanzadeh

Time: 9h00, Wednesday, September 25, 2019,
Location:
Room 611-612, Building A6, Institute of Mathematics
Abstract:
  Let $R$ be a commutative Noetherian local ring.

The well-known result of Foxby, Reiten and Sharp is that $R$ admits a dualizing module if and only if $R$ is Cohen-Macaulay and a homomorphic image of a local Gorenstein ring.

In 2012, Jorgensen, Leuschke and Sather-Wagstaff characterize the Cohen-Macaulay local rings which admit dualizing modules and non-trivial semidualizing modules.

In this talk we are going to investigate a Cohen-Macaulay ring $R$ which admits a dualizing module and a suitable chain of semidualizing modules.

We will also see that the Cohen-Macaulay ring $R$ can not admit suitable chains of arbitrary length. Indeed, the length of a suitable chain of semidualizing $R$-modules is less than the generalized

Loewy length of $R$. This talk is based on joint work with Mohammad T. Dibaei.

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