Generalized perfect numerical semigroups

Mohammad Zmmo and Nesrin Tutaş
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 1, Pages 150–162
DOI: 10.7546/nntdm.2024.30.1.150-162
Full paper (PDF, 461 Kb)

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Authors and affiliations

Mohammad Zmmo
Department of Mathematics, Akdeniz University
07058, Antalya, Turkey

Nesrin Tutaş
Department of Mathematics, Akdeniz University
07058, Antalya, Turkey

Abstract

In this work, we study the isolated gaps for generalized numerical semigroups, introduce generalized perfect numerical semigroups, and exemplify these semigroups. In particular, we reveal the effects of the perfectness condition on a generalized Weierstrass semigroup.

Keywords

• Numerical semigroups
• Generalized numerical semigroups
• Perfect semigroups

2020 Mathematics Subject Classification

• Primary: 20M75
• Secondary: 20M14, 11D07

References

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Manuscript history

• Received: 22 March 2023
• Revised: 3 March 2024
• Accepted: 8 March 2024
• Online First: 12 March 2024

Copyright information

Ⓒ 2024 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).