Presentations of rings with a chain of semidualizing modules

Abstract

Inspired by Jorgensen et. al., it is proved that if a Cohen--Macaulay local ring $R$ with dualizing module admits a suitable chain of semidualizing $R$--modules of length $n$, then $R\cong Q/(I_1+\cdots +I_n)$ for some Gorenstein ring $Q$ and ideals $I_1,\cdots ,I_n$ of $Q$; and, for each $\Lambda \subseteq [n]$, the ring $Q/({\Sigma }_{l\in \Lambda }{I}_l)$ has some interesting cohomological properties . This extends the result of Jorgensen et. al., and also of Foxby and Reiten.

18 pages, To appear in Mathematica Scandinavica