Vol. 7, No. 1, 2014

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ISSN: 1944-4184 (e-only)
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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