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IRREDUCIBILITY IN THE SET OF NUMERICAL SEMIGROUPS WITH FIXED MULTIPLICITY

V. BLANCO

Departamento de Álgebra, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

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and

J. C. ROSALES

Departamento de Álgebra, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

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https://doi.org/10.1142/S0218196711006492Cited by:4 (Source: Crossref)

Abstract

In this paper we introduce the notion of m-irreducibility that extends the standard concept of irreducibility of a numerical semigroup when the multiplicity is fixed. We analyze the structure of the set of m-irreducible numerical semigroups, we give some properties of these numerical semigroups and we present algorithms to compute the decomposition of a numerical semigroup with multiplicity m into m-irreducible numerical semigroups.

Keywords:

AMSC: 20M14, 13H10

References

R. Apéry, C. R. Acad. Sci. Paris 222, 1198 (1946). Web of Science, Google Scholar
V. Barucci, D. E. Dobbs and M. Fontana, Mem. Amer. Math. Soc. 125, 598 (1997). Google Scholar
V. Barucci and R. Froberg, J. Algebra 188, 418 (1997), DOI: 10.1006/jabr.1996.6837. Crossref, Web of Science, Google Scholar
M. Delgado, P. A. García-Sánchez and J. Morais, "Numericalsgps": A GAP Package on Numerical Semigroups, http://www.gap-system.org/Packages/numericalsgps.html . Google Scholar
E. Kunz, Proc. Amer. Math. Soc. 25, 748 (1973), DOI: 10.1090/S0002-9939-1970-0265353-7. Crossref, Web of Science, Google Scholar
J. C. Rosales and M. B. Branco, B. Belg. Math. Soc-Sim. 9, 373 (2002). Web of Science, Google Scholar
J. C. Rosales and M. B. Branco, J. Pure Appl. Algebra 171(3), 303 (2002), DOI: 10.1016/S0022-4049(01)00128-1. Crossref, Web of Science, Google Scholar
J. C. Rosaleset al., Semigroup Forum 67, 145 (2003), DOI: 10.1007/s00233-002-0007-3. Crossref, Web of Science, Google Scholar
J. C. Rosales and M. B. Branco, Pacific J. Math. 209, 131 (2003), DOI: 10.2140/pjm.2003.209.131. Crossref, Web of Science, Google Scholar
J. C. Rosales and P. A. García-Sanchez , Numerical Semigroups ( Springer , New York , 2009 ) . Crossref, Google Scholar