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The trace of the canonical module of a Cohen-Macaulay ring describes itsnon-Gorenstein locus. We study the trace of the canonical module of a Segreproduct of algebras, and we apply our results to compute the non-Gorensteinlocus of toric rings. We provide several sufficient and necessary conditionsfor Hibi rings and normal semigroup rings to be Gorenstein on the puncturedspectrum.

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