Presentations of rings with a chain of semidualizing modules

2014/12/23 by Amanzadeh, Ensiyeh, Dibaei, Mohammad T.
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.7465

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/(I₁+⋯+I_n) for some Gorenstein ring Q and ideals I₁,⋯, I_n 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.

Related

• Presentations of rings with non-trivial semidualizing modules
• Local cohomology modules and Gorenstein injectivity with respect to a semidualizing module
• Chains of semidualizing modules
• Linkage of modules with respect to a semidualizing module
• Semidualizing Modules over Numerical Semigroup Rings