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THE SHORT RESOLUTION OF A SEMIGROUP ALGEBRA

Part of: Algorithms - Computer Science Computational aspects and applications Commutative algebra: Homological methods Special varieties

Published online by Cambridge University Press:  29 August 2017

I. OJEDA Open the ORCID record for I. OJEDA [Opens in a new window]  and
A. VIGNERON-TENORIO Open the ORCID record for A. VIGNERON-TENORIO [Opens in a new window]
I. OJEDA
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, E-06071 Badajoz, España email ojedamc@unex.es
A. VIGNERON-TENORIO*
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, E-11405 Jerez de la Frontera (Cádiz), España email alberto.vigneron@uca.es
*
✉alberto.vigneron@uca.es
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Abstract

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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.

Keywords

free resolutionBetti numbersemigroup algebraaffine semigroupApéry setFrobenius problem

MSC classification

Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 14M25: Toric varieties, Newton polyhedra 68W30: Symbolic computation and algebraic computation
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 3 , December 2017 , pp. 400 - 411
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

Both authors are partially supported by the projects MTM2012-36917-C03-01 and MTM2015-65764-C3-1-P (MINECO/FEDER, UE), National Plan I+D+I. The first author is also partially supported by Junta de Extremadura (FEDER funds) and the second by Junta de Andalucía (group FQM-366).

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