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...

maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem. in this paper, we apply fuzzy soft sets to  -hyperrings. the concept of ( , q )       -fuzzy soft  -hyperideals of  -hyperrings is first introduced. some new characterizations are investigated. in particular, a...

$!!!!$ in this paper, the notion of fuzzy $!$ krasner $!(m, n)$-hyperrings($!f^{(m, n)}!$-hyperrings) by using the notion of$f^m$-hyperoperations and $f^n$-operations is introduced and somerelated properties are investigated. in this regards,relationships between krasner $f^{(m, n)}$-hyperrings and krasner$(m, n)$-hyperrings are considered. we shall prove that everykrasner $f^{(m, n)}$-hyperrin...