This paper is focused on numerical semigroups and presents a simple construction, that we call "dilatation", which, from a starting semigroup S, permits to get an infinite family of semigroups which share several properties with S. The invariants of each semigroup T of this family are given in terms of the corresponding invariants of S and both the Apéry set and the minimal generators of T are described. We also study three properties that are close to the Gorenstein property of the associated semigroup ring: almost Gorenstein, 2-AGL, and nearly Gorenstein properties. More precisely, we prove that S satisfies one of these properties if and only if each dilatation of S satisfies the corresponding one.
Dilatations of numerical semigroups / Barucci, V.; Strazzanti, F.. - In: SEMIGROUP FORUM. - ISSN 0037-1912. - STAMPA. - 98:2(2019), pp. 251-260. [10.1007/s00233-018-9922-9]
Dilatations of numerical semigroups
Barucci, V.;
2019
Abstract
This paper is focused on numerical semigroups and presents a simple construction, that we call "dilatation", which, from a starting semigroup S, permits to get an infinite family of semigroups which share several properties with S. The invariants of each semigroup T of this family are given in terms of the corresponding invariants of S and both the Apéry set and the minimal generators of T are described. We also study three properties that are close to the Gorenstein property of the associated semigroup ring: almost Gorenstein, 2-AGL, and nearly Gorenstein properties. More precisely, we prove that S satisfies one of these properties if and only if each dilatation of S satisfies the corresponding one.File | Dimensione | Formato | |
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Barucci_Dilatations_2019.pdf
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