A note on the lattice of fuzzy hyperideals of a hyperring

Bayrak, Dilek; Yamak, Sultan

doi:10.1007/s13370-017-0511-y

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2021

2022

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Cited by 2 publications

(2 citation statements)

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“…Ameri and Motameni [24] applied fuzzy set theory to the hyperideals of fuzzy hyperrings. Bayrak and Yamak [25] introduced some results on the lattice of fuzzy hyperideals of a hyperring. Davvaz [26] studied fuzzy Krasner (m, n)hyperrings.…”

Section: Introductionmentioning

confidence: 99%

Topological Structures of Lower and Upper Rough Subsets in a Hyperring

Abughazalah

Yaqoob

Shahzadi

2021

Journal of Mathematics

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Section: Introductionmentioning

confidence: 99%

Topological Structures of Lower and Upper Rough Subsets in a Hyperring

Abughazalah

Yaqoob

Shahzadi

2021

Journal of Mathematics

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“…A class of hyperrings is multiplicative hyperring which satisfies the axioms similar a ring, but product replaced by hyperproduct. The multiplicative hyperring defined by Rota in 1982 and its properties have been studied by many mathematicians [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

On Hyperideals of Multiplicative Hyperrings

COŞGUN

Acar

2022

Cumhuriyet Science Journal

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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.

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A note on the lattice of fuzzy hyperideals of a hyperring

Cited by 2 publications

References 10 publications

Topological Structures of Lower and Upper Rough Subsets in a Hyperring

Topological Structures of Lower and Upper Rough Subsets in a Hyperring

On Hyperideals of Multiplicative Hyperrings

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