The arithmetic extensions of a numerical semigroup. Issue 9 (1st September 2020)

• Record Type: Journal Article
• Authors: Ojeda, I.; Rosales, J. C.
• Is Part Of: Communications in algebra. Volume 48:Issue 9(2020)
• Page Start: 3707
• Page End: 3715
• Publication Date: 2020-09-01
• Subjects: Apery set -- arithmetic extension -- extension -- Frobenius number -- genus -- Kunz-coordinates -- numerical semigroup -- quotient of a semigroup; 20M14 -- 11D07; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1744159
• Languages: English
• ISSNs: 0092-7872

Abstract

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.