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The trace of the canonical module

Research paper by Jürgen Herzog, Takayuki Hibi, Dumitru I. Stamate

Indexed on: 08 Dec '16Published on: 08 Dec '16Published in: arXiv - Mathematics - Commutative Algebra



Abstract

The trace of the canonical module (the canonical trace) determines the non-Gorenstein locus of a local Cohen-Macaulay ring. We call a local Cohen-Macaulay ring nearly Gorenstein, if its canonical trace contains the maximal ideal. Similar definitions can be made for positively graded Cohen-Macaulay $K$-algebras. We study the canonical trace for tensor products and Segre products of algebras, as well as of (squarefree) Veronese subalgebras. The results are used to classify the nearly Gorenstein Hibi rings. We also consider the canonical trace of one-dimensional rings with a focus on numerical semigroup rings.