University of Guilan Journal of Algebra and Related Topics 2345-3931 8 2 2020 12 01 Relations between G-sets and their associate G^{\hat}-sets 75 91 4422 10.22124/jart.2020.17806.1232 EN N. Rakhsh Khorshid Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran S. Ostadhadi-Dehkordi Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran Journal Article 2020 09 27 In this paper, we define and consider $G$-set on<br />$\Gamma$-semihypergroups and we obtain relations between $G$-sets<br />and their associate $\widehat{G}$-sets where $G$ is a<br />$\Gamma$-semihypergroup and $\widehat{G}$ is an associated<br />semihypergroup. Finally, we obtain the relation between direct limit of $\widehat{G}$-sets from the direct limit defined on<br /> $G$-sets. https://jart.guilan.ac.ir/article_4422_2ba69b51a111a29742107433b92aaab6.pdf