An Approach to Numerical Semigroups

Year 2010, Volume: 39 Issue: 3, 411 - 415, 01.03.2010

Sedat İlhan

Abstract

In this paper, we give some results on principal ideals of a numerical semigroup S = hs1, s2, . . . , spi for p ≥ 2, p ∈ N. We also describe some relations between Apery subsets and ideals of S.

Keywords

Numerical semigroup, Apery set, Ideal, Gap, 2000 AMS Classification: 20 M 14

References

• Barucci, V., Dobbs, D. E. and Fontana, M. Maximality properties in numerical semigroups and applications to one-dimensional analyticalle irreducible local domains, Memoirs of The Amer. Math. Soc. 598, 13–25, 1997.
• Madero-Craven, M. and Herzinger, K. Apery set of numerical semigroups, Communications in Algebra 33, 3831–3838, 2005.
• Rosales, J. C. Numerical semigroups with Apery sets of unique expression, Journal of Algebra 226, 479–487, 2000.
• Rosales, J. C. and Garcia-Sanchez, P. A. Finitely Generated Commutative Monoids (Nova Science Publishers, New York, 1999).
• Rosales, J. C., Garcia-Sanchez, P. A. and Garcia-Garcia, J. I. Irreducible ideals of finitely generated commutative monoids, Journal of Algebra 238, 328–344, 2001.
• Rosales, J. C., Garcia-Sanchez, P. A., Garcia-Garcia, J. I. and Jimenez Madrid, J. A. Funda- mental gaps in numerical semigroups, Journal of Pure and Applied Algebra 189, 301–313, 2004.