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MODULAR DIOPHANTINE INEQUALITIES AND ROTATIONS OF NUMERICAL SEMIGROUPS

Part of: Semigroups Diophantine equations

Published online by Cambridge University Press:  01 June 2008

M. DELGADO  and
J. C. ROSALES
M. DELGADO
Affiliation:
Centro de Matemática, Universidade do Porto, Rua do Campo Alegre 687 4169-007 Porto, Portugal (email: [email protected])
J. C. ROSALES*
Affiliation:
Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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For a numerical semigroup S, a positive integer a and a nonzero element m of S, we define a new numerical semigroup R(S,a,m) and call it the (a,m)-rotation of S. In this paper we study the Frobenius number and the singularity degree of R(S,a,m). Moreover, we observe that the rotations of ℕ are precisely the modular numerical semigroups.

Keywords

numerical semigroupsDiophantine inequalityFrobenius numbersingularity degree

MSC classification

Secondary: 20M14: Commutative semigroups 11D75: Diophantine inequalities
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 3 , June 2008 , pp. 315 - 328
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

The first author gratefully acknowledges support of the FCT through the CMUP. The second author was supported by the project MTM2004-01446 and FEDER founds.

References

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