Research Article
BibTex RIS Cite

Year 2022, , 672 - 675, 27.12.2022

Betül Coşgun , Ummahan Merdinaz Acar

https://doi.org/10.17776/csj.1022963

Abstract

Keywords

Multiplicative hyperring n-hyperideal δ-n-hyperideal.

Supporting Institution

Muğla Sıtkı Koçman University

Project Number

(21/124/03/01)

References

  • [1] Marty F., Sur une generalization de la notion de groupe, 8. Congress Math. Scandenaves, Stockholm, (1934) 45-49.
  • [2] Corsini S., Leoreanu V., Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publishers, (2003).
  • [3] Corsini S., Prolegomena of Hypergroup Theory, Aviani Editore, Italy, (1993).
  • [4] Davvaz B., Leoreanu-Fotea V., Hyperring Theory and Applications. Palm Harbor, USA: International Academic Press (2007).
  • [5] Rota R., Sugli iperanelli moltiplicativi, Rend. Di. Math., Series VII, 4 (1982) 711-724.
  • [6] Ameri R., Eyvazi M., Hoskova-Mayerova S., Superring of Polynomials over a Hyperring, Mathematics, 7 (10) (2019) 1-15.
  • [7] Davvaz B., Salasi A., A Realization of Hyperrings, Communications in Algebra, 34(2007) 4389-4400.
  • [8] Ameri R., Eyvazi M., Hoskova-Mayerova S., Multiplicative Hyperring of Fractions and Coprime Hyperideals, An. St. Univ. Ovidius Constant, 25(1) (2017) 5-23.
  • [9] Bayrak D., Yamak S., A Note on The Lattice of Fuzzy Hyperideals of a Hyperring, Afrika Matematika, 28(2017) 1185-1192.
  • [10] Procesi R., Rota R., On Some Classes of Hyperstructures, Discrete Mathematics, 208/209 (1999) 485-497.
  • [11] Ameri R., Kordi A., Clean Multiplicative Hyperrings, Italian Journal of Pure and Applied Mathematics, 35 (2015) 625-636.
  • [12] Dasgupta U., On Prime and Primary Hyperideals of a Multiplicative Hyperrings, Annals of the Alexandru Ioan Cuza University-Mathematics, LVIII (1) (2012) 19-36.
  • [13] Ulucak G., On Expansions of Prime and 2-absorbing Hyperideals in Multiplicative Hyperrings, Turkish Journal of Mathematics, 43 (2019) 1504-1517.
  • [14] Tekir U., Koç S., Oral K.H., N-ideals of Commutative Rings, Filomat, (2017) 2933-2941.
  • [15] Coşgun B., Acar U. A Study on Hyperideals of Multiplicative Hyperring, IFSCOM 2021, Antalya, Türkiye, (2021).
  • [16] Anbarloei M., On Almost Primary Hyperideals and Almost 2-Absorbing Primary Hyperideals of a Multiplicative Hyperring, Southeast Asian Bulletin of Mathematics, 44 (2020) 167-176.

On Hyperideals of Multiplicative Hyperrings

Year 2022, , 672 - 675, 27.12.2022

Betül Coşgun , Ummahan Merdinaz Acar

https://doi.org/10.17776/csj.1022963

Abstract

Let R be a commutative multiplicative hyperring. In this paper, we introduce and study the concepts of n-hyperideal and
δ-n-hyperideal of R which are generalization of n-ideals and
δ-n-ideals of the in a commutative ring. An element a is called a nilpotent element of R if there exists a positive integer n such that 0∈a^n. A hyperideal I (I ≠R) of R is called an n- hyperideal of R if for all a,b∈R, a*b⊆I and a is non-nilpotent element implies that b∈I [15]. Also, I is called a
δ-n-hyperideal if for all a,b∈R, a*b⊆I then either a is nilpotent or b∈δ(I) , where
δ is an expansion function over the set of all hyperideals of a multiplicative hyperring. In addition, we give the definition of zd-hyperideal. Some properties of n-hyperideals,
δ-n-hyperideals and zd-hyperideals of the hyperring R are presented. Finally, the relations between these notions are investigated.

Keywords

Multiplicative hyperring n-hyperideal δ-n-hyperideal.

Project Number

(21/124/03/01)

References

  • [1] Marty F., Sur une generalization de la notion de groupe, 8. Congress Math. Scandenaves, Stockholm, (1934) 45-49.
  • [2] Corsini S., Leoreanu V., Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publishers, (2003).
  • [3] Corsini S., Prolegomena of Hypergroup Theory, Aviani Editore, Italy, (1993).
  • [4] Davvaz B., Leoreanu-Fotea V., Hyperring Theory and Applications. Palm Harbor, USA: International Academic Press (2007).
  • [5] Rota R., Sugli iperanelli moltiplicativi, Rend. Di. Math., Series VII, 4 (1982) 711-724.
  • [6] Ameri R., Eyvazi M., Hoskova-Mayerova S., Superring of Polynomials over a Hyperring, Mathematics, 7 (10) (2019) 1-15.
  • [7] Davvaz B., Salasi A., A Realization of Hyperrings, Communications in Algebra, 34(2007) 4389-4400.
  • [8] Ameri R., Eyvazi M., Hoskova-Mayerova S., Multiplicative Hyperring of Fractions and Coprime Hyperideals, An. St. Univ. Ovidius Constant, 25(1) (2017) 5-23.
  • [9] Bayrak D., Yamak S., A Note on The Lattice of Fuzzy Hyperideals of a Hyperring, Afrika Matematika, 28(2017) 1185-1192.
  • [10] Procesi R., Rota R., On Some Classes of Hyperstructures, Discrete Mathematics, 208/209 (1999) 485-497.
  • [11] Ameri R., Kordi A., Clean Multiplicative Hyperrings, Italian Journal of Pure and Applied Mathematics, 35 (2015) 625-636.
  • [12] Dasgupta U., On Prime and Primary Hyperideals of a Multiplicative Hyperrings, Annals of the Alexandru Ioan Cuza University-Mathematics, LVIII (1) (2012) 19-36.
  • [13] Ulucak G., On Expansions of Prime and 2-absorbing Hyperideals in Multiplicative Hyperrings, Turkish Journal of Mathematics, 43 (2019) 1504-1517.
  • [14] Tekir U., Koç S., Oral K.H., N-ideals of Commutative Rings, Filomat, (2017) 2933-2941.
  • [15] Coşgun B., Acar U. A Study on Hyperideals of Multiplicative Hyperring, IFSCOM 2021, Antalya, Türkiye, (2021).
  • [16] Anbarloei M., On Almost Primary Hyperideals and Almost 2-Absorbing Primary Hyperideals of a Multiplicative Hyperring, Southeast Asian Bulletin of Mathematics, 44 (2020) 167-176.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Betül Coşgun 0000-0003-1389-259X

Ummahan Merdinaz Acar 0000-0001-5762-9684

Project Number (21/124/03/01)
Publication Date December 27, 2022
Submission Date November 14, 2021
Acceptance Date October 18, 2022
Published in Issue Year 2022

Cite

APA Coşgun, B., & Acar, U. M. (2022). On Hyperideals of Multiplicative Hyperrings. Cumhuriyet Science Journal, 43(4), 672-675. https://doi.org/10.17776/csj.1022963