%0 Journal Article
%T Application of fundamental relations on n-ary polygroups
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Mirvakili, S.
%A Davvaz, B.
%D 2012
%\ 04/01/2012
%V 38
%N 1
%P 169-184
%! Application of fundamental relations on n-ary polygroups
%K Hypergroup
%K polygroup
%K $n$-ary
hypergroup
%K $n$-ary polygroup
%K derived $n$-ary subgroup
%K fundamental relation
%R
%X The class of $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{\"o}rnte $n$-arygroups and a generalization of polygroups. The$\beta^*$-relation and the $\gamma^*$-relation are the smallestequivalence relations on an $n$-ary polygroup $P$ such that$P/\beta^*$ and $P/\gamma^*$ are an $n$-ary group and acommutative $n$-ary group, respectively. We use the $\beta^*$-relation and the $\gamma^*$-relation on a given$n$-ary polygroup and obtain some new results and somefundamental theorems in this respect. In particular, we prove that the relation $\gamma$ is transitive on an $n$-arypolygroup.
%U http://bims.iranjournals.ir/article_398_343a6bc9bb99db6c78480f38fbc278d8.pdf