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 $R\cong Q\mathrm{/}(I_1+\cdots +I_n)$ for some Gorenstein ring $Q$ and ideals $I_1,\cdots ,I_n$ of $Q$; and, for each $\mathrm{\Lambda }\subseteq [n]$, the ring $Q\mathrm{/}({\mathrm{\Sigma }}_{l\in \mathrm{\Lambda }}{I}_l)$ has some interesting cohomological properties . This extends the result of Jorgensen et. al., and also of Foxby and Reiten.