A Note on The Some Class of Symmetric Numerical Semigroups

Öz

In this article, we will examine some classes of symmetric numerical semigroups and half of them, which are a class of irreducible numerical semigroups such that U= and U= symmetric numerical semigroups, respectively.

Anahtar Kelimeler

• Numerical semigroup
• Gap
• Perfect
• Symmetric
• Irreducible numerical semigroup

Öz

Bu makalede, indirgenemez sayısal yarıgrupların bir sınıfı olan sırasıyla 𝑼 =< 𝒂, 𝒂 + 𝟏 > ve 𝑼 =< 𝒂, 𝒂 + 𝟐 > şeklindeki simetrik sayısal yarıgrupları ve onların yarısı olan sayısal yarıgrupları inceleyeceğiz.

Anahtar Kelimeler

• Sayısal yarıgrup
• Boşluk
• Mükemmel
• Simetrik
• İndirgenemez sayısal yarıgrup

Kaynakça

1. Ojeda, I., Vigneron-Tenorio, A., Simplicial complexes and minimal free resolution of monomial algebras, Journal of Pure and Applied Algebra, 214, 850–861, 2010.
2. Bertin, J., Carbonne, P., Semi-groupes d’entiers et application aux branches, Journal of Algebra, 49, 81–95, 1977.
3. Delorme, C., Sous-monoïdes d’intersection complète de N, Annales Scientifiques de l'École Normale Supérieure, 4(9), 145–154, 1976. Watanabe, K. Some examples of one dimensional Gorenstein domains, Nagoya Mathematical Journal, 49, 101–109, 1973.
4. Rosales, J.C., Branco, M.B., Irreducible numerical semigroups, Pacific Journal Of Mathematics, 209(1), 131-143, 2003.
5. Blanco, V., Rosales, J.C., m-irreducible numerical semigroups, Forum Mathematicum, 25, 1249 – 1261, 2013.
6. Süer, M., Yeşil, M., Symmetric and pseudo-symmetric numerical semigroups via young diagrams and their semigroup rings, Journal of the Korean Mathematical Society, 58 (6), 1367- 1383, 2021.
7. Barucci, V., Dobbs, D.E., Fontana, M., Maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains, Memoirs of the American Mathematical Society 598, 1997.
8. Delgado, M., Farrán, J.I., García-Sánchez, P.A., Llena, D., On the weight hierarchy of codes coming from semigroups with two generators, IEEE Transactions on Information Theory, 60, 282–295, 2014.

9. Froberg, R., Gotlieb C., Haggkvist, R., On numerical semigroups, Semigroup Forum, 35, 63-68, 1997.
10. Rosales J.C., Garcia-Sanchez, P.A., Developments in Mathematics Series Numerical semigroups., Springer New York, 181 pp, 2009. Assi A., Garcia-Sanchez, P.A., RSME Springer Series Numerical semigroups and Applications, Springer New York, 106 pp, 2016.
11. Rosales, J.C., Symmetric numerical semigroups with arbitrary multiplicity and embedding dimension, Proceedings of the American Mathematical Society, 129(8), 2197-2203, 2001.
12. Rosales J.C., Garcia-Sanhez, P.A., Pseudo-symmetric numerical semigroups with three generators, Journal of Algebra, 291, 46-54, 2005.
13. Harold, J.S., Numerical semigroups that are fractions of numerical semigroups of maximal embedding dimension, JP Journal of Algebra Number Theory and App., 17(1), 69-96, 2010.
14. Harold, J.S., On isolated gaps in numerical semigroups, Turkish Journal of Mathematics, 46,123 –129, 2022.
15. Frias, M.A.M., Rosales, J.C., Perfect numerical semigroups, Turkish Journal of Mathematics, 43, 1742 – 1754, 2019.
16. İlhan, S., On the set gaps in numerical semigroups, International Journal of Algebra, 1(3), 145-149, 2007.