@article {
author = {Mirvakili, S. and Davvaz, B.},
title = {Application of fundamental relations on n-ary polygroups},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {38},
number = {1},
pages = {169-184},
year = {2012},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {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.},
keywords = {Hypergroup,polygroup,$n$-ary
hypergroup,$n$-ary polygroup,derived $n$-ary subgroup,fundamental relation},
url = {http://bims.iranjournals.ir/article_398.html},
eprint = {http://bims.iranjournals.ir/article_398_343a6bc9bb99db6c78480f38fbc278d8.pdf}
}