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

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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.

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