ON RELATION OF ALTERNATIVE LA-SEMIGROUP

Abstract

In this paper, we establish the relation of alternative LA-semigroup with existence subclasses of LA-semigroup. We prove that under what condition a left alternative LA-semigroup becomes right alternative, flexible, left, right and middle nuclear square LA-semigroups. By the use of Modern mathematical technique GAP and Mace4 we construct a non-associative example that left alternative is neither contain in right alternative, flexible, left, right and middle nuclear square LA-semigroups. Although left(right) alternative LA-semigroup is non-associative, but we prove that the combination of T¹ and T⁴− LA-semigroups it becomes associative. We also find the relation of right alternative, Jordan, stein, LA*,LC, RC, middle and right nuclear square LA-semigroups.