Open Access
2019 Duality on value semigroups
Philipp Korell, Mathias Schulze, Laura Tozzo
J. Commut. Algebra 11(1): 81-129 (2019). DOI: 10.1216/JCA-2019-11-1-81


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.


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Philipp Korell. Mathias Schulze. Laura Tozzo. "Duality on value semigroups." J. Commut. Algebra 11 (1) 81 - 129, 2019.


Published: 2019
First available in Project Euclid: 13 March 2019

zbMATH: 07037590
MathSciNet: MR3922427
Digital Object Identifier: 10.1216/JCA-2019-11-1-81

Primary: 14H20
Secondary: 13C14 , 20M12

Keywords: canonical module , curve singularity , Duality , value semigroup

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

Vol.11 • No. 1 • 2019
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