Breakable Semihypergroups

Abstract

In this paper, we introduce and characterize the breakable semihypergroups, a natural generalization of breakable semigroups, defined by a simple property: every nonempty subset of them is a subsemihypergroup. Then, we present and discuss on an extended version of Rédei’s theorem for semi-symmetric breakable semihypergroups, proposing a different proof that improves also the theorem in the classical case of breakable semigroups.

Special Issue on Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures

“…The theoretical aspects discussed in the articles of this book are principally related with three main topics: (semi)hypergroups, hyperfields and BCK-algebras. Heidari and Cristea [11] present a natural generalization of breakable semigroups, defining a new hypercompositional structure called a breakable semihypergroup, where every non-empty subset is a subsemihypergroup. The authors proved that a hypergroup is breakable if and only if it is a B-hypergroup.…”

Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures

“…Recall that Massouros and Mittas [18,19] called such hypergroups B-hypergroups, where B stands for binary, while Chvalina [9,20] called them minimal extensive hypergroups. They have been recently used also in the study of breakable semihypergroups [21].…”

Factorizable Ordered Hypergroupoids with Applications

“…Breakable semihypergroups were firstly presented by Heidari and Cristea [11] in 2019. In a breakable semihypergroup, each nonempty subset is a subsemihypergroup.…”