Generalized hyperideals in locally associative left almost semihypergroups

In this paper, we introduce the concept of a locally associative LA-semihypergroup by generalizing the idea of a locally associative LA-semigroup given in Mushtaq–Yusuf, 1979, and study an (m,n)regular class of a locally associative LA-semihypergroup. We give some examples to connect an LA-semihypergroup with commutative hypergroups and commutative semihypergroups. We also characterize a locally associative LA-semihypergroup H in terms of (m,n)-hyperideals and prove that if R(L) is a 0-minimal right (left) hyperideal of H, then either R ◦L = {0} or R ◦L is a 0-minimal (m,n)-hyperideal of H for m,n ≥ 2.