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 ∼ = Q/(I 1 + · · · + In) for some Gorenstein ring Q and ideals I 1 , · · · , In of Q; and, for each Λ ⊆ [n], the ring Q/(Σ l∈Λ I l ) has some interesting cohomological properties . This extends the result of Jorgensen et. al., and also of Foxby and Reiten. 2010 Mathematics Subject Classification. 13D05, 13D07.

Chains of semidualizing modules

“…[13], characterize the Cohen-Macaulay local rings which admit dualizing modules and non-trivial semidualizing modules. Recently, Amanzadeh and Dibaei [1], characterize the Cohen-Macaulay local rings which admit dualizing modules and suitable chains of semidualizing modules.…”