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Papers β€Ί Characterizing affine π’ž-semigroups

Characterizing affine π’ž-semigroups

7 Jul 2019arXiv:1907.03276links table onlyarchive 2025-07-28

J. D. DΓ­az-RamΓ­rez, J. I. GarcΓ­a-GarcΓ­a, D. MarΓ­n-AragΓ³n, A. Vigneron-Tenorio

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Let π’ž βŠ‚β„•α΅– be a finitely generated integer cone and SβŠ‚π’ž be an affine semigroup such that the real cones generated by π’ž and by S are equal. The semigroup S is called π’ž-semigroup if π’žβˆ–S is a finite set. In this paper, we characterize the π’ž-semigroups from their minimal generating sets, and we give an algorithm to check if S is a π’ž-semigroup and to compute its set of gaps. We also study the embedding dimension of π’ž-semigroups obtaining a lower bound for it, and introduce some families of π’ž-semigroups whose embedding dimension reaches our bound. In the last section, we present a method to obtain a decomposition of a π’ž-semigroup into irreducible π’ž-semigroups.

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