N-ARY HYPERGROUPS

Document Type: Regular Paper

Authors

1 1Department of Mathematics, Yazd University, Yazd, I. R. of Iran

2 School of Science and Education, Democritus University of Thrace, Alexandroupolis, Greece

Abstract

In this paper the class of n-ary hypergroups is introduced and several properties are found and
examples are presented. n-ary hypergroups are a generalization of hypergroups in the sense of Marty. On the
other hand, we can consider n-ary hypergroups as a good generalization of n-ary groups. We define the
fundamental relation β* on an n-ary hypergroup H as the smallest equivalence relation such that H / β* is
the n-ary group, and then some related properties are investigated.

Keywords