THE SHORT RESOLUTION OF A SEMIGROUP ALGEBRA

@article{Ojeda2015THESR,
  title={THE SHORT RESOLUTION OF A SEMIGROUP ALGEBRA},
  author={Ignacio Ojeda and Alberto Vigneron-Tenorio},
  journal={Bulletin of the Australian Mathematical Society},
  year={2015},
  volume={96},
  pages={400 - 411}
}
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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