Existence of non-associative algebraic hyper-structures and related problems. (Q497034)

A left almost semigroup (\(\mathcal{LA}\)-semigroup) is a groupoid \(S\) whose elements satisfy the following law \((ab)c=(cb)a\) for all \(a,b,c\in S\). Hila and Dine generalized this concept to algebraic hyperstructures and introduced the notion of \(\mathcal{LA}\)-semihypergroups. In this paper, the authors show that a non-associative \(\mathcal{LA}\)-semihypergroup exists even if it has right identity. Also, congruence relations and homomorphisms between \(\mathcal{LA}\)-semihypergroups are studied.