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

Keywords

• LA-semihypergroup,left invertive law,pure left identity and 0minimal hyperideals

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23. Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad- PAKISTAN E-mail address: [e-mail] 2School of Mathematical Sciences, University of Science and Technology of China, Hefei-CHINA E-mail address: [e-mail]