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Year 2023, Volume: 13 Issue: 1&2, 18 - 27, 31.12.2023

Ahmet Çelik

https://doi.org/10.37094/adyujsci.1229288

Abstract

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.

Keywords

Sayısal yarıgrup Boşluk Mükemmel Simetrik İndirgenemez sayısal yarıgrup

References

  • Ojeda, I., Vigneron-Tenorio, A., Simplicial complexes and minimal free resolution of monomial algebras, Journal of Pure and Applied Algebra, 214, 850–861, 2010.
  • Bertin, J., Carbonne, P., Semi-groupes d’entiers et application aux branches, Journal of Algebra, 49, 81–95, 1977.
  • 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.
  • Rosales, J.C., Branco, M.B., Irreducible numerical semigroups, Pacific Journal Of Mathematics, 209(1), 131-143, 2003.
  • Blanco, V., Rosales, J.C., m-irreducible numerical semigroups, Forum Mathematicum, 25, 1249 – 1261, 2013.
  • 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.
  • 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.
  • 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.
  • Froberg, R., Gotlieb C., Haggkvist, R., On numerical semigroups, Semigroup Forum, 35, 63-68, 1997.
  • 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.
  • Rosales, J.C., Symmetric numerical semigroups with arbitrary multiplicity and embedding dimension, Proceedings of the American Mathematical Society, 129(8), 2197-2203, 2001.
  • Rosales J.C., Garcia-Sanhez, P.A., Pseudo-symmetric numerical semigroups with three generators, Journal of Algebra, 291, 46-54, 2005.
  • 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.
  • Harold, J.S., On isolated gaps in numerical semigroups, Turkish Journal of Mathematics, 46,123 –129, 2022.
  • Frias, M.A.M., Rosales, J.C., Perfect numerical semigroups, Turkish Journal of Mathematics, 43, 1742 – 1754, 2019.
  • İlhan, S., On the set gaps in numerical semigroups, International Journal of Algebra, 1(3), 145-149, 2007.

A Note on The Some Class of Symmetric Numerical Semigroups

Year 2023, Volume: 13 Issue: 1&2, 18 - 27, 31.12.2023

Ahmet Çelik

https://doi.org/10.37094/adyujsci.1229288

Abstract

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.

Keywords

Numerical semigroup Gap Perfect Symmetric Irreducible numerical semigroup

References

  • Ojeda, I., Vigneron-Tenorio, A., Simplicial complexes and minimal free resolution of monomial algebras, Journal of Pure and Applied Algebra, 214, 850–861, 2010.
  • Bertin, J., Carbonne, P., Semi-groupes d’entiers et application aux branches, Journal of Algebra, 49, 81–95, 1977.
  • 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.
  • Rosales, J.C., Branco, M.B., Irreducible numerical semigroups, Pacific Journal Of Mathematics, 209(1), 131-143, 2003.
  • Blanco, V., Rosales, J.C., m-irreducible numerical semigroups, Forum Mathematicum, 25, 1249 – 1261, 2013.
  • 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.
  • 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.
  • 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.
  • Froberg, R., Gotlieb C., Haggkvist, R., On numerical semigroups, Semigroup Forum, 35, 63-68, 1997.
  • 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.
  • Rosales, J.C., Symmetric numerical semigroups with arbitrary multiplicity and embedding dimension, Proceedings of the American Mathematical Society, 129(8), 2197-2203, 2001.
  • Rosales J.C., Garcia-Sanhez, P.A., Pseudo-symmetric numerical semigroups with three generators, Journal of Algebra, 291, 46-54, 2005.
  • 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.
  • Harold, J.S., On isolated gaps in numerical semigroups, Turkish Journal of Mathematics, 46,123 –129, 2022.
  • Frias, M.A.M., Rosales, J.C., Perfect numerical semigroups, Turkish Journal of Mathematics, 43, 1742 – 1754, 2019.
  • İlhan, S., On the set gaps in numerical semigroups, International Journal of Algebra, 1(3), 145-149, 2007.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Ahmet Çelik 0000-0001-5980-0625

Publication Date December 31, 2023
Submission Date January 4, 2023
Acceptance Date July 6, 2023
Published in Issue Year 2023 Volume: 13 Issue: 1&2

Cite

APA Çelik, A. (2023). A Note on The Some Class of Symmetric Numerical Semigroups. Adıyaman University Journal of Science, 13(1&2), 18-27. https://doi.org/10.37094/adyujsci.1229288
AMA Çelik A. A Note on The Some Class of Symmetric Numerical Semigroups. ADYU J SCI. December 2023;13(1&2):18-27. doi:10.37094/adyujsci.1229288
Chicago Çelik, Ahmet. “A Note on The Some Class of Symmetric Numerical Semigroups”. Adıyaman University Journal of Science 13, no. 1&2 (December 2023): 18-27. https://doi.org/10.37094/adyujsci.1229288.
EndNote Çelik A (December 1, 2023) A Note on The Some Class of Symmetric Numerical Semigroups. Adıyaman University Journal of Science 13 1&2 18–27.
IEEE A. Çelik, “A Note on The Some Class of Symmetric Numerical Semigroups”, ADYU J SCI, vol. 13, no. 1 & 2, pp. 18–27, 2023, doi: 10.37094/adyujsci.1229288.
ISNAD Çelik, Ahmet. “A Note on The Some Class of Symmetric Numerical Semigroups”. Adıyaman University Journal of Science 13/1 & 2 (December 2023), 18-27. https://doi.org/10.37094/adyujsci.1229288.
JAMA Çelik A. A Note on The Some Class of Symmetric Numerical Semigroups. ADYU J SCI. 2023;13:18–27.
MLA Çelik, Ahmet. “A Note on The Some Class of Symmetric Numerical Semigroups”. Adıyaman University Journal of Science, vol. 13, no. 1&2, 2023, pp. 18-27, doi:10.37094/adyujsci.1229288.
Vancouver Çelik A. A Note on The Some Class of Symmetric Numerical Semigroups. ADYU J SCI. 2023;13(1&2):18-27.
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