ON PURE LA-SEMIHYPERGROUPS

Abstract

We generalize the existing theory of an associative structure [6] bystudying it in a non-associative hyper-structure called an LA-semihypergroup.The results obtained will also generalize the results on LA-semigroup withouthyper theory. As an application of our results we characterize (0, 2)-hyperidealsof an LA-semihypergroup H and prove that A is a (0, 2)-hyperideal of H ifand only if A is a left hyperideal of some left hyperideal of H. We also showthat an LA-semihypergroup H is 0-(0, 2)-bisimple if and only if H is right0-simple. Finally we give the connection of ordered and hyper theories of anLA-semigroup