Vol. 7, No. 1, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Homogenization of a nonsymmetric embedding-dimension-three numerical semigroup

Seham Abdelnaby Taha and Pedro A. García-Sánchez

Vol. 7 (2014), No. 1, 77–96
Abstract

Let n1,n2,n3 be positive integers with gcd(n1,n2,n3) = 1. For S = n1,n2,n3 nonsymmetric, we give an alternative description, using elementary techniques, of a minimal presentation of its homogenization S̄ = (1,0),(1,n1),(1,n2),(1,n3). As a consequence, we show that this minimal presentation is unique. We recover Bresinsky’s characterization of the Cohen–Macaulay property of S̄ and present a procedure to compute all possible catenary degrees of the elements of S̄.

Keywords
numerical semigroup, catenary degree, projective monomial curve, homogeneous catenary degree
Mathematical Subject Classification 2010
Primary: 20M14, 20M25
Milestones
Received: 25 February 2013
Revised: 2 May 2013
Accepted: 1 June 2013
Published: 24 October 2013

Communicated by Scott T. Chapman
Authors
Seham Abdelnaby Taha
Departamento de Álgebra
Facultad de Ciencias
Universidad de Granada
Av. Fuentenueva, s/n
18071 Granada
Spain
Pedro A. García-Sánchez
Departamento de Álgebra
Facultad de Ciencias
Universidad de Granada
Av. Fuentenueva, s/n
18071 Granada
Spain