TY - JOUR
ID - 398
TI - Application of fundamental relations on n-ary polygroups
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Mirvakili, S.
AU - Davvaz, B.
AD - Payame Noor University
AD - Yazd University
Y1 - 2012
PY - 2012
VL - 38
IS - 1
SP - 169
EP - 184
KW - Hypergroup
KW - polygroup
KW - $n$-ary
hypergroup
KW - $n$-ary polygroup
KW - derived $n$-ary subgroup
KW - fundamental relation
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_398.html
L1 - http://bims.iranjournals.ir/article_398_343a6bc9bb99db6c78480f38fbc278d8.pdf
ER -