The aim of this research work is to define a new class hyperstructure as generalization semigroups, semihypergroups and Γ-semihypergroups that we call (Δ,G)-sets. Also, fundamental relation on (Δ,G)-sets prove some results in respect. Then, introduce the notions quotient by using congruence relations. Finally, concept complete parts Noetherian(Artinian)

In this paper, the concepts of hybrid pure hyperideals in ordered hypersemigroups are introduced and some algebraic properties studied. We characterize weakly regular terms hyperideals. Finally, we introduce prove that if such satisfy idempotent property.

In previous our research, the concepts of visible submodules and fully modules were introduced, then these two fuzzified to fuzzy fuzzy. The main goal this paper is study relationships between some types such as semiprime, prime, quasi, divisible, F-regular, quasi injective, duo modules, where under certain conditions it has been proven that each module duo. addition, there are many various pro...

The semilattice equivalence relations play an important role in investigating the structural properties of ordered semihypergroups. Such can be expressed terms hyperfilters. There are two concepts (ordered) hyperfilters semihypergroups which were introduced by Tang et al. [16] and Kehayopulu[9]. In this paper, we prove that those coincide characterize least on Furthermore, investigate relations...

Let R be a prime ring with a right generalized (α, β)derivation f and let a ∈ R. Suppose that af(x)n = 0 for all x ∈ R, where n is a fixed positive integer. Then af(x) = 0 for all x ∈R. In particular, if f is either a regular right generalized (α, β)-derivation or a nonzero generalized (α, β)-derivation, then a = 0. In [13] I. N. Herstein proved that if R is a prime ring and d is an inner deriv...

let $g$ be a group with identity $e$. let $r$ be a $g$-graded commutative ring with a non-zero identity and $m$ be a graded $r$-module. in this article, we introduce the concept of graded almost semiprime submodules. also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.