@article { author = {Heidari, D. and Davvaz, B.}, title = { -hypergroups and  -semihypergroups associated to binary relations}, journal = {Iranian Journal of Science}, volume = {35}, number = {2}, pages = {69-80}, year = {2011}, publisher = {Springer}, issn = {2731-8095}, eissn = {2731-8109}, doi = {10.22099/ijsts.2011.2130}, abstract = {The concept of  -semihypergroups is a generalization of semigroups, a generalization of semihypergroups and a generalization of  -semigroups. In this paper, we study the concept of semiprime ideals in a  -semihypergroup and prove some results. Also, we introduce the notion of  -hypergroups and closed  -subhypergroups. Finally, we study the concept of  -semihypergroups associated to binary relations and give necessary and sufficient conditions on a set of binary relations  on a non-empty set S such that S becomes a  -semihypergroup or a  -hypergroup}, keywords = {hypergroup,semihypergroup, -semigroup, -semihypergroup,binary relation}, url = {https://ijsts.shirazu.ac.ir/article_2130.html}, eprint = {https://ijsts.shirazu.ac.ir/article_2130_87c2127ceaf5eff87e853ab29e370914.pdf} }