A Hyperstructures Approach to the Direct Limit and Tensor Product for Left(right) G-sets on Hypergroups

In this paper, we introduce the concept of left(right)-G sets by external hyperoperations and some examples presented. We construct quotient left(right)-G sets by regular (strongly) regular relations. Also, we consider fundamental relation as a smallest strongly regular relations and by complete parts concepts introduce an equivalence relation that is coincide with fundamental relation. The main purpose of this paper is to introduce the concepts of tensor product and direct limit on G-sets of n-ary semihypergroups that are non-additive modification of classical construction in module theory. This concept is crucially important in homological algebra and several properties are found and examples are presented.