2019
DOI: 10.1007/s11856-019-1898-y
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The trace of the canonical module

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… Show more

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Cited by 78 publications
(120 citation statements)
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“…In particular, when each R i is Gorenstein, we get the following result, which is a slight generalization of Theorem 4.15 in [HHS19].…”
Section: The Trace Of the Canonical Module For Segre Productsmentioning
confidence: 52%
See 3 more Smart Citations
“…In particular, when each R i is Gorenstein, we get the following result, which is a slight generalization of Theorem 4.15 in [HHS19].…”
Section: The Trace Of the Canonical Module For Segre Productsmentioning
confidence: 52%
“…In this section we develop some of the algebraic tools which will be used in the next section, and introduce trace ideals. We refer to [HHS19] for a more complete introduction of the trace of the canonical module.…”
Section: The Trace Of the Canonical Module For Segre Productsmentioning
confidence: 99%
See 2 more Smart Citations
“…The concepts of generalized Gorenstein and nearly Gorenstein rings are defined in [12] and [20], respectively. Here we prove that nearly Gorenstein rings have canonical reductions.…”
Section: Introductionmentioning
confidence: 99%