Vol. 220, No. 1, 2005

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Correction to: Modular Diophantine inequalities and numerical semigroups

J. C. Rosales, P. A. García-Sánchez and J. M. Urbano-Blanco

Vol. 220 (2005), No. 1, 199

Correction to Pacific Journal of Mathematics 218 (2005) 379–398


Volume 218:2 (2005), 379–398

The modular numerical semigroup S(2,6) = 〈3,4,5〉 is pseudo-symmetric. Thus Corollary 60 of the paper is false, since it asserts that S(a,ab) is not pseudo-symmetric for any positive integers a,b > 1. The mistake comes from part (ii) of Proposition 58, which should read

S is pseudo-symmetric if and only if (a−1,b) + (a−1) mod b = b−1.

(The sign on right-hand side of this equality was incorrect.)

Milestones
Received: 21 March 2005
Published: 1 May 2005
Authors
J. C. Rosales
Departamento de Álgebra
Universidad de Granada
E-18071 Granada
Spain
P. A. García-Sánchez
Departamento de Álgebra
Universidad de Granada
E-18071 Granada
Spain
J. M. Urbano-Blanco
Departamento de Álgebra
Universidad de Granada
E-18071 Granada
Spain