Journal of Commutative Algebra

Duality on value semigroups

Philipp Korell, Mathias Schulze, and Laura Tozzo

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Abstract

We establish a combinatorial counterpart of the Cohen-Macaulay duality on a class of curve singularities which includes algebroid curves. For such singularities the value semigroup and the value semigroup ideals of all fractional ideals satisfy axioms that define so-called good semigroups and good semigroup ideals. We prove that each good semigroup admits a canonical good semigroup ideal which gives rise to a duality on good semigroup ideals. We show that the Cohen-Macaulay duality and our good semigroup duality are compatible under taking values.

Article information

Source
J. Commut. Algebra, Volume 11, Number 1 (2019), 81-129.

Dates
First available in Project Euclid: 13 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.jca/1552464134

Digital Object Identifier
doi:10.1216/JCA-2019-11-1-81

Mathematical Reviews number (MathSciNet)
MR3922427

Zentralblatt MATH identifier
07037590

Subjects
Primary: 14H20: Singularities, local rings [See also 13Hxx, 14B05]
Secondary: 13C14: Cohen-Macaulay modules [See also 13H10] 20M12: Ideal theory

Keywords
Curve singularity value semigroup canonical module duality

Citation

Korell, Philipp; Schulze, Mathias; Tozzo, Laura. Duality on value semigroups. J. Commut. Algebra 11 (2019), no. 1, 81--129. doi:10.1216/JCA-2019-11-1-81. https://projecteuclid.org/euclid.jca/1552464134


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