On Factorizable Semihypergroups

Abstract

<jats:p>In this paper, we define and study the concept of the factorizable semihypergroup, i.e., a semihypergroup that can be written as a hyperproduct of two proper sub-semihypergroups. We consider some classes of semihypergroups such as regular semihypergroups, hypergroups, regular hypergroups, and polygroups and investigate their factorization property.</jats:p>

Transposition Regular TA-Groupoids and Their Structures

“…In future research, we will use the levels of implicativities the TA-groupoids to study the relationships between the TA-groupoids and the related logic algebras (as shown in [29,30]). In [31,32], Heidari and Cristea studied the breakable semihypergroups and the factorizable semihypergroups. We have proved that every left transposition regular TA-groupoid is a semigroup (see Theorem 5).…”

Factorizable Ordered Hypergroupoids with Applications

“…Recently, much attention has been paid to investigating the factorizable hyperstructures. In [13], Heidari and Cristea have suggested the concept of factorizable semihypergroups by using the concept of factorizable semigroups [14]. In this regard, Munir et al [15] initiated the study of factorizable hypergroupoids and discussed their properties.…”

“…In this regard, Munir et al [15] initiated the study of factorizable hypergroupoids and discussed their properties. For future work, one could extend the existing works [13,15] to the framework of fuzzy sets.…”

Hypergroupoids as Tools for Studying Blood Group Genetics

“…A hypergroupoid H is said to be factorizable if, for a proper subhypergroupoid C of the hypergroupoid H, there exists another proper subhypergroupoid D of H having at least one distinct element from C, such that C • D = H. The pair (C, D) is called the factorization of H with factors C and D[12] and[13].If the identity e ∈ H, pair (e, H) is a factorization of H. The factorization of a hypergroupoid is not unique, as indicated by Example 4.2.…”