k. p. shum

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 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.