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 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2016
- DOI:
- 10.48550/arXiv.1612.02723
- arXiv:
- arXiv:1612.02723
- Bibcode:
- 2016arXiv161202723H
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Combinatorics;
- Mathematics - Rings and Algebras;
- 13H10;
- 13D02;
- 05E40 (Primary);
- 14M25;
- 13A02;
- 13F20;
- 06A11 (Secondary)
- E-Print:
- v3: minor changes to Sections 3 and 4. Theorem 6.6 is new. The last part in v2 dealing with numerical semigroups is separated into another paper