Application of (m, n)-Г-Hyperideals in Characterization of LA-Г-Semihypergroups

Abstract

In this paper, we study the concept of ordered (m, n)-Г-hyperideals in an ordered LA-Г-semihypergroup. We show that if (S, Г, ◦,⩽) is a unitary ordered LA-Г-semihypergroup with zero 0 and satisfies the hypothesis that it contains no non-zero nilpotent (m, n)-Г-hyperideals and if R(L) is a 0-minimal right (left) Г-hyperideal of S, then either (R◦ Г ◦L] = {0} or (R◦ Г ◦ L] is a 0-minimal (m, n)-Г-hyperideal of S. Also, we prove that if (S, Г, ◦,⩽) is a unitary ordered LA-Г-semihypergroup; A is an (m, n)-Г-hyperideal of S and B is an (m, n)-Г-hyperideal of A such that B is idempotent, then B is an (m, n)-Г-hyperideal of S.

Keywords

• la-semihypergroups
• (m, n)-г-hyperideals
• ordered la-г-semi-hypergroups
• 16d25
• 20m10
• 20n99