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The short resolution of a semigroup algebra Ojeda, Ignacio Vigneron Tenorio, Alberto Free resolutions Resoluciones libres Betti number Número de Betti Affine semigroups Semigrupos afines Producción Científica 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. Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (projects MTM2012-36917-C03-01 / MTM2015-65764-C3-1-P) 2020-04-06T16:14:28Z 2020-04-06T16:14:28Z 2017 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Bulletin of the Australian Mathematical Society, 2017, vol. 96, n. 3. p. 400-411 1755-1633 http://uvadoc.uva.es/handle/10324/40726 10.1017/S0004972717000612 eng https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/short-resolution-of-a-semigroup-algebra/1CF99F51F65D3A8E17E8EF5F205DAC21 Attribution-NonCommercial-NoDerivatives 4.0 Internacional info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2017 Cambridge University Press application/pdf Cambridge University Press https://uvadoc.uva.es/bitstream/10324/40726/4/Short-resolution-of-semigroup-algebra.pdf.jpg Hispana TEXT http://creativecommons.org/licenses/by-nc-nd/4.0/ UVaDOC. Repositorio Documental de la Universidad de Valladolid http://uvadoc.uva.es/handle/10324/40726