The short resolution of a semigroup Algebra

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URI: http://hdl.handle.net/10498/33967

DOI: 10.1017/S0004972717000612

ISSN: 1755-1633

ISSN: 0004-9727

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Author/s
Ojeda, Ignacio; Vigneron Tenorio, AlbertoAuthority UCA
Date
2017
Department
Matemáticas
Source
Bulletin of the Australian Mathematical Society - 2017, Vol. 96 n. 3 pp. 400-411
Abstract
This work generalises the short resolution given by Pisón Casares ['The short resolution of a lattice ideal', Proc. Amer. Math. Soc. 131(4) (2003), 1081-1091] to any affine semigroup. We give a characterisation of Apéry sets which provides a simple way to compute Apéry sets of affine semigroups and Frobenius numbers of numerical semigroups. We also exhibit a new characterisation of the Cohen-Macaulay property for simplicial affine semigroups.
Subjects
free resolution; Betti number; semigroup algebra; affine semigroup; Apery set; Frobenius problem
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional
This work is under a Creative Commons License Attribution-NonCommercial-NoDerivatives 4.0 Internacional