s. ostadhadi dehkordi

In this paper, the notion of H-sets on Hv-groups is introduced and some related properties are investigated and some examples are given. In this regards, the concept of regular, strongly regular relations and homomorphism of H-sets are adopted. Also, the classical isomorphism theorems of groups are generalized to H-sets on Hv-groups. Finally, by using these concepts tensor product on Hv-groups is introduced andproved that the tensor product exists and is unique up to isomorphism.

We first define a new concept, namely, the ΓUP-algebra. Then, we study and investigate the properties of its ΓUP-ideals and ΓUP-subalgebras. As a consequence, we construct a covariant functor between the ΓUP-category and the UP algebra-category. Some possible connections between these categories are also considered.

In this paper, we define and consider G-set on Γsemihypergroups and we obtain relations between G-sets and their associate Gb-sets where G is a Γ-semihypergroup and Gb is an associated semihypergroup. Finally, we obtain the relation between direct limit of Gb-sets from the direct limit defined on G-sets.

In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups .Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper.

The concept of Γ-semihyperrings is a generalization of a semiring, a generalization of a Γ-semiring, and a generalization of a semihyperering. In this paper, we define the notions of complex product, extension property and flat Γ-semihyperrings and some of their properties are obtained. In addition, we prove that every flat Γ-semihyperring is absolutely extendable. Finally, we give some characterization of stable elements.