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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| Published in | Israel journal of mathematics Vol. 233; no. 1; pp. 133 - 165 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Jerusalem
The Hebrew University Magnes Press
01.08.2019
Springer Nature B.V |
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| 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 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. |
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| AbstractList | 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. 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. |
| Author | Stamate, Dumitru I. Hibi, Takayuki Herzog, Jürgen |
| Author_xml | – sequence: 1 givenname: Jürgen surname: Herzog fullname: Herzog, Jürgen organization: Fachbereich Mathematik, Universität Duisburg-Essen – sequence: 2 givenname: Takayuki surname: Hibi fullname: Hibi, Takayuki organization: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University – sequence: 3 givenname: Dumitru I. surname: Stamate fullname: Stamate, Dumitru I. email: dumitru.stamate@fmi.unibuc.ro organization: ICUB/Faculty of Mathematics and Computer Science, University of Bucharest |
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| Snippet | 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... |
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| SubjectTerms | Algebra Analysis Applications of Mathematics Group Theory and Generalizations Mathematical and Computational Physics Mathematics Mathematics and Statistics Modules Rings (mathematics) Tensors Theoretical |
| Title | The trace of the canonical module |
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