Measuring primality in numerical semigroups with embedding dimension three-Reference-Cited by-同舟云学术

Measuring primality in numerical semigroups with embedding dimension three

Published:2015-09-07 Issue:01 Volume:15 Page:1650007
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Chapman S. T.¹,García-Sánchez P. A.²,Tripp Z.³,Viola C.⁴

Affiliation:

1. Sam Houston State University, Department of Mathematics and Statistics, Box 2206, Huntsville, TX 77341-2206, USA

2. Departamento de Álgebra and CITIC-UGR, Universidad de Granada, E-18071 Granada, España

3. Tufts University, Department of Mathematics, 503 Boston Avenue, Bromfield-Pearson, Room 103, Medford, MA 02155, USA

4. Dipartimento di Matematica e Informatica, Viale A. Doria, 6 – I 95125, Catania, Italia

Abstract

In this paper, we find the ω-value of the generators of any numerical semigroup with embedding dimension three. This allows us to determine all possible orderings of the ω-values of the generators. In addition, we relate the ω-value of the numerical semigroup to its catenary degree.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498816500079

Reference17 articles.

1. HOW FAR IS AN ELEMENT FROM BEING PRIME?

2. ON BOUNDING MEASURES OF PRIMENESS IN INTEGRAL DOMAINS

3. An algorithm to compute ω-primality in a numerical monoid

4. Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids

5. THE CATENARY AND TAME DEGREES ON A NUMERICAL MONOID ARE EVENTUALLY PERIODIC

Cited by 8 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Complement-Finite Ideals;Algebraic, Number Theoretic, and Topological Aspects of Ring Theory;2023

2. On Delta Sets Of Some Pseudo-Symmetric Numerical Semigroups With Embedding Dimension Three;Bitlis Eren Üniversitesi Fen Bilimleri Dergisi;2022-02-22

3. When Is a Puiseux Monoid Atomic?;The American Mathematical Monthly;2021-03-23

4. Multiplicative factorization in numerical semigroups;International Journal of Algebra and Computation;2019-11-18

5. The system of sets of lengths and the elasticity of submonoids of a finite-rank free commutative monoid;Journal of Algebra and Its Applications;2019-07-23