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THE SHORT RESOLUTION OF A SEMIGROUP ALGEBRA

  • I. OJEDA (a1) and A. VIGNERON-TENORIO (a2)
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.

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Corresponding author
alberto.vigneron@uca.es
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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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[1] Briales, E., Campillo, A., Marijuán, C. and Pisón, P., ‘Minimal systems of generators for ideals of semigroups’, J. Pure Appl. Algebra 124 (1998), 730.
[2] Briales, E., Campillo, A., Pisón, P. and Vigneron, A., ‘Simplicial complexes and syzygies of lattice ideals’, in: Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering (South Hadley, MA, 2000), Contemporary Mathematics, 286 (American Mathematical Society, Providence, RI, 2001), 169183.
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[14] Roune, B. H., ‘Solving thousand-digit Frobenius problems using Gröbner bases’, J. Symbolic Comput. 43(1) (2008), 17.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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