Measuring the non-Gorenstein locus of Hibi rings and normal affine semigroup rings

Abstract

The trace of the canonical module of a Cohen-Macaulay ring describes its non-Gorenstein locus. We study the trace of the canonical module of a Segre product of algebras, and we apply our results to compute the non-Gorenstein locus of toric rings. We provide several sufficient and necessary conditions for Hibi rings and normal semigroup rings to be Gorenstein on the punctured spectrum.

References in corpus (2)

• The Frobenius complexity of Hibi rings
• Anticanonical modules of Segre products

Cited by in corpus (3)

• Trace of canonical modules, annihilator of Ext, and classes of rings close to being Gorenstein
• Non-Gorenstein loci of Ehrhart rings of chain and order polytopes
• Stable set rings which are Gorenstein on the punctured spectrum