The aim of this paper is the study of fuzzy $Gamma$-hyperrings. In thisregard the notion of -fuzzy hyperideals of $Gamma$-hyperrings are introduced andbasic properties of them are investigated. In particular, the representationtheorem for $nu$-fuzzy hyperideals are given and it is shown that the image of a-fuzzy hyperideal of a $Gamma$-hyperring under a certain conditions is two-valued.Finally,...

We consider the fundamental relation on a semihypergroup to interpret the lower and upper approximations as subsets of the fundamental semigroup / and we give some results in this connection. Also, we introduce the notion of a bi-hyperideal to study the relationship between approximations and bi-hyperideals.

In this paper, we introduce the concept of a locally associative LA-semihypergroup by generalizing the idea of a locally associative LA-semigroup given in Mushtaq–Yusuf, 1979, and study an (m,n)regular class of a locally associative LA-semihypergroup. We give some examples to connect an LA-semihypergroup with commutative hypergroups and commutative semihypergroups. We also characterize a locall...

The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. D-radicals of ideals are introduced and investigated. In particular, the prime radi...

We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propo...

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, ...

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, ...