The class of $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{\"o}rnte $n$-ary groups and a generalization of polygroups. The $\beta^*$-relation and the $\gamma^*$-relation are the smallest equivalence relations on an $n$-ary polygroup $P$ such that $P/\beta^*$ and $P/\gamma^*$ are an $n$-ary group and a commutative $n$-ary group, respectively. We use the $\beta^*$-relation and the $\gamma^*$-relation on a given $n$-ary polygroup and obtain some new results and some fundamental theorems in this respect. In particular, we prove that the relation $\gamma$ is transitive on an $n$-ary polygroup.
Mirvakili, S. & Davvaz, B. (2012). Application of fundamental relations on n-ary polygroups. Bulletin of the Iranian Mathematical Society, 38(1), 169-184.
MLA
Mirvakili, S., & Davvaz, B. "Application of fundamental relations on n-ary polygroups", Bulletin of the Iranian Mathematical Society, 38, 1, 2012, 169-184.
HARVARD
Mirvakili S., Davvaz B. (2012). 'Application of fundamental relations on n-ary polygroups', Bulletin of the Iranian Mathematical Society, 38(1), pp. 169-184.
CHICAGO
S. Mirvakili & B. Davvaz, "Application of fundamental relations on n-ary polygroups," Bulletin of the Iranian Mathematical Society, 38 1 (2012): 169-184,
VANCOUVER
Mirvakili S., Davvaz B. Application of fundamental relations on n-ary polygroups. BIMS. 2012;38(1):169-184.
