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.

Let $G$ be a monoid with identity $e$. In this paper, first we introduce the notions of $G$-graded hyperrings, graded hyperideals and graded hyperfields in the sense of Krasner hyperring $R$. Also, we define the notion of a greded $R$-hypermodules and some examples are presented. Then we investigate graded maximal, graded prime and graded primary hyperideals of a graded hyperring $R$. Finally, ...

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...

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...

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...

Let R be a commutative hyperring with identity. We introduceand study prime fuzzy hyperideals of R. We investigate the Zariski topologyon FHspec(R), the spectrum of prime fuzzy hyperideals of R.

In this paper, we introduce the concept of 1-absorbing prime hyperideals which is an expansion hyperideals. Several properties are provided. For example, it proved that if a strong C-hyperideal I id="M2"> R not prime, then id="M3"> local multiplicative hyperring. Moreover, and study notions primary hyperideals, ...

Abstract The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of normal First we define concept zero-divisors over hypermodule based it introduce class hypermodules, one divisible After presenting some their fundamental properties, will show that R -hypermodules M coincide whenever hyperring with no . Finally...