Generalized numerical semigroups: the first properties and some other developments

SEMINARIO DE ÁLGEBRA

Conferenciante: Carmelo Cisto (University of Messina)

Abstract: Let \(\mathbb{N}\) be the set of non negative integers and \(d\) be a positive integer. A generalized numerical semigroup (GNS) is a submonoid \(S\) of \(\mathbb{N}^d\) such that the set \(\mathbb{N}^d \setminus S\) is finite. Generalized numerical semigroups have been introduced in 2016 by Failla, Peterson and Utano as a straightforward generalization of the well known concept of numerical semigroup, that is a submonoid of \(\mathbb{N}\) having finite complement in it. Subsequently, other papers appeared and some researches was developed with the aim to generalize to the context of GNSs some notions and results concerning numerical semigroups. For instance the notions of irreducibility, almost-symmetry and Wilf's conjecture were introduced also in this more general context. In this talk we recall this notions in the setting of GNSs, and we have a look to some other recent developments in the existing literature.