EN
On Hyperideals of Multiplicative Hyperrings
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.
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
Supporting Institution
Muğla Sıtkı Koçman University
Project Number
(21/124/03/01)
References
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- [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.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Betül Coşgun
0000-0003-1389-259X
Türkiye
Publication Date
December 27, 2022
Submission Date
November 14, 2021
Acceptance Date
October 18, 2022
Published in Issue
Year 1970 Volume: 43 Number: 4