A hyperstructures approach to the direct limit and tensor product for left(right) G-sets on hypergroups

In this paper, we introduce the concept left(right)-G sets by external hyperoperations and some examples presented. We construct quotientleft(right)-G sets by regular (strongly) regular relations. Also, we considerfundamental relation as a smallest strongly regular relations and by completeparts concepts introduce an equivalence relation that is coincide with fundamentalrelation. The main purpose of this paper is to introduce the conceptsof tensor product and direct limit on G-sets of n-ary semihypergroups thatare non-additive modication of classical construction in module theory. Thisconcept is crucially important in homological algebra and several propertiesare found and examples are presented