{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T22:01:54Z","timestamp":1759010514888},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2018,3]]},"abstract":"<jats:p> Value semigroups of non-irreducible singular algebraic curves and their fractional ideals are submonoids of [Formula: see text] that are closed under infimums, have a conductor and fulfill a special compatibility property on their elements. Monoids of [Formula: see text] fulfilling these three conditions are known in the literature as good semigroups and there are examples of good semigroups that are not realizable as the value semigroup of an algebraic curve. In this paper, we consider good semigroups independently from their algebraic counterpart, in a purely combinatorial setting. We define the concept of good system of generators, and we show that minimal good systems of generators are unique. Moreover, we give a constructive way to compute the canonical ideal and the Arf closure of a good subsemigroup when [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196718500091","type":"journal-article","created":{"date-parts":[[2018,1,15]],"date-time":"2018-01-15T09:41:27Z","timestamp":1516009287000},"page":"179-206","source":"Crossref","is-referenced-by-count":11,"title":["Good subsemigroups of \u2115n"],"prefix":"10.1142","volume":"28","author":[{"given":"Marco","family":"D\u2019Anna","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica e Informatica, Viale A. Doria, 6 - I 95125 Catania, Italia"}]},{"given":"Pedro A.","family":"Garc\u00eda-S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Departamento de \u00c1lgebra and IEMath-GR, Universidad de Granada, E-18071 Granada, Espa\u00f1a"}]},{"given":"Vincenzo","family":"Micale","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica e Informatica, Viale A. Doria, 6 - I 95125 Catania, Italia"}]},{"given":"Laura","family":"Tozzo","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universita\u2019 degli Studi di Genova, Via Dodecaneso 35 - I 16154 - Genova, Italia"}]}],"member":"219","published-online":{"date-parts":[[2018,3,27]]},"reference":[{"key":"S0218196718500091BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(98)00160-1"},{"key":"S0218196718500091BIB002","doi-asserted-by":"publisher","DOI":"10.1080\/00927870008827044"},{"issue":"2","key":"S0218196718500091BIB003","first-page":"219","volume":"3","author":"Barucci V.","year":"2003","journal-title":"J. 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