On atoms of the set of generalized numerical semigroups with fixed corner element

Autor:	Bernardini, Matheus, Castellanos, Alonso S., Tenório, Wanderson, Tizziotti, Guilherme
Rok vydání:	2023
Předmět:	Mathematics - Group Theory Mathematics - Combinatorics Primary 20M14 Secondary 06F05 11D07
Druh dokumentu:	Working Paper
Popis:	We study the so-called atomic GNS, which naturally extends the concept of atomic numerical semigroup. We introduce the notion of corner special gap and we characterize the class of atomic GNS in terms of the cardinality of the set of corner special gaps and also in terms of a maximal property. Using this maximal property we present some properties concerning irreducibility of Frobenius GNSs. In particular, we provide sufficient conditions for certain Frobenius GNSs to be an atom non-irreducible (ANI). Furthermore, we given necessary and sufficient conditions so that the maximal elements of a set of Frobenius GNSs with two fixes gaps to be all irreducible or not. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.13506 Zobrazit plný text záznamu View this record from Arxiv