English

The arithmetic extensions of a numerical semigroup

Commutative Algebra 2020-03-31 v2 Group Theory

Abstract

In this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of arithmetic extension of a given numerical semigroup. As by-product, new explicit formulas for the Frobenius number and the genus of proportionally modular semigroups are obtained.

Keywords

Cite

@article{arxiv.2003.05193,
  title  = {The arithmetic extensions of a numerical semigroup},
  author = {Ignacio Ojeda and José Carlos Rosales},
  journal= {arXiv preprint arXiv:2003.05193},
  year   = {2020}
}

Comments

This article has been accepted for publication in Communications in Algebra, published by Taylor & Francis

R2 v1 2026-06-23T14:11:21.437Z