Over the years, different types of hyperideals have been introduced in order to let us fully realize structures hyperrings general. The aim this research work is define and characterize a new class Krasner $(m,n)$-hyperring that we call n-ary $J$-hyperideals. A proper hyperideal $Q$ with scalar identity $1_R$ said be an $J$-hyperideal if whenever $x_1^n \in R$ such $g(x_1^n) Q$ $x_i \notin J_{(...

¡v in this paper we consider a strongly regular relation ƒá on hypermodules so that the quotient is amodule (with abelian group) over a fundamental commutative ring. also, we state necessary and sufficientconditions so that the relation ƒá is transitive, and finally we prove that ƒá is transitive on hypermodules.

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Let G be an abelian group with identity e. R a graded multiplicative hyperring and ? : Igr(R) expansion function of Igr(R), where is the set all hyperideals R. In this paper, we introduce study concepts ?-primary 2-absorbing which are extended classes prime 2- absorbing R, respectively. Moreover, give basic properties these new types investigate relations among structures.

In this article we give the definition of weakly prime hyperideals over multiplicative hyperring. We provide important results showing relations between and hyperideals. Then n-hyperideal (1,n) hyperideal hyperrings. investigate their properties some examples. Hyperstructures are very topic because it satisfy to study multidisiplinary. Especially in chemistry, coding theory, geometry, artificia...

Krasner hyperrings are a generalization of rings. Indeed, in hyperring the addition is hyperoperation, while multiplication an ordinary operation. On other hand, rough set theory near theory. Now, this paper we interested combining these concepts. We study and investigate notion on nearness approximation space. Also, define subhyperring, hyperideal, homomorphism prove some results present sever...

Definition 1.1. If S is a multiplicative subset of a ring A (commutative with 1), the quotient hyperring A/mS = (A/mS,+, ·,−, 0, 1) is defined as follows: A/mS is the set of equivalence classes with respect to the equivalence relation ∼ on A defined by a ∼ b iff as = bt for some s, t ∈ S. The operations on A/mS are the obvious ones induced by the corresponding operations on A: Denote by a the e...