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Extensions of n-ary prime hyperideals via an n-ary multiplicative subset in a Krasner (m,n)-hyperring
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Let R be a Krasner (m, n)-hyperring and S be an n-ary multiplicative subset
of R. The purpose of this paper is to introduce the notion of n-ary S-prime
hyperideals as a new expansion of n-ary prime hyperideals. A hyperideal I of
R disjoint with S is said to be an n-ary S-prime hyperideal if there exists
s ? S such that whenever 1(xn1) ? I for all xn1 ? R, then 1(s,xi,1(n?2))
? I for some 1 ? i ? n. Several properties and characterizations concerning
n-ary S-prime hyperideals are presented. The stability of this new concept
with respect to various hyperring-theoretic constructions are studied.
Furthermore, the concept of n-ary S-primary hyperideals is introduced.
Several properties of them are provided.
Title: Extensions of n-ary prime hyperideals via an n-ary multiplicative subset in a Krasner (m,n)-hyperring
Description:
Let R be a Krasner (m, n)-hyperring and S be an n-ary multiplicative subset
of R.
The purpose of this paper is to introduce the notion of n-ary S-prime
hyperideals as a new expansion of n-ary prime hyperideals.
A hyperideal I of
R disjoint with S is said to be an n-ary S-prime hyperideal if there exists
s ? S such that whenever 1(xn1) ? I for all xn1 ? R, then 1(s,xi,1(n?2))
? I for some 1 ? i ? n.
Several properties and characterizations concerning
n-ary S-prime hyperideals are presented.
The stability of this new concept
with respect to various hyperring-theoretic constructions are studied.
Furthermore, the concept of n-ary S-primary hyperideals is introduced.
Several properties of them are provided.
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