Presentations of rings with a chain of semidualizing modules

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.