[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.
[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,
Volume: 43 Issue: 4, 672 - 675, 27.12.2022
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.
[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.
[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.
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