The trace of the canonical module

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...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 233; no. 1; pp. 133 - 165
Main Authors Herzog, Jürgen, Hibi, Takayuki, Stamate, Dumitru I.
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.08.2019
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Modules
Rings (mathematics)
Tensors
Theoretical
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Summary: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 study connections between the class of nearly Gorenstein rings and that of almost Gorenstein rings. We show that in dimension one, the former class includes the latter.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-019-1898-y