On Minimal and Maximal Hyperidealsin n-ary Semihypergroups

Abstract

The concept of j-hyperideals, for all positive integers 1≤j≤n and n≥2, in n-ary semihypergroups, is a generalization of the concept of left, lateral and right hyperideals in ternary semihypergroups. In this paper, we first introduce the concept of j-(0-)simple n-ary semihypergroups and discuss their related properties through terms of j-hyperideals. Furthermore, we characterize the minimality and maximality of j-hyperideals in n-ary semihypergroups and establish the relationships between the (0-)minimal, maximal j-hyperideals and the j-(0-)simple n-ary semihypergroups. Our main results are to extend and generalize the results on semihypergroups and ternary semihypergroups. Moreover, a related question raised by Petchkaew and Chinram is solved.

A Study onA−I−Γ-Hyperideals andm,n−Γ-Hyperfilters in OrderedΓ-Semihypergroups

“…Semihypergroups are as important in algebraic hyperstructures as the semigroups in algebraic structures. Recently, Daengsaen et al [12] studied minimal and maximal hyperideals of n-ary semihypergroups. Ordered semihypergroups were introduced by Heidari and Davvaz [13] as a generalization of the ordered semigroups.…”

Regularities in Ordered n-Ary Semihypergroups

“…In [25], Hila et al introduced the concept of j-hyperideals of n-ary semihypergroups, which is a generalization of j-ideals of n-ary semigroups, and discussed the related properties. The interesting properties of j-hyperideals in ternary semihypergroups and n-ary semihypergroups can be found in [26,27]. The left regularity, right regularity, intra-regularity, and complete regularity of ternary semihypergroups in terms of various j-hyperideals were characterized by Naka et al [28,29].…”