Upper bound on the colength of the trace of the canonical module in dimension one
J\"urgen Herzog, Shinya Kumashiro
TL;DR
This paper investigates the maximum possible colength of the trace of the canonical module in one-dimensional Cohen-Macaulay rings, providing answers to previously posed questions in the field.
Contribution
It establishes an upper bound for the colength of the trace of the canonical module and addresses open questions by Herzog-Hibi-Stamate and Kobayashi.
Findings
Established an explicit upper bound for the colength.
Provided affirmative answers to two open questions.
Enhanced understanding of the structure of canonical modules in dimension one.
Abstract
We study the upper bound of the colength of trace of the canonical module in one-dimensional Cohen-Macaulay rings. We answer the two questions posed by Herzog-Hibi-Stamate and Kobayashi.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras