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ISRN Algebra
Volume 2011 (2011), Article ID 953124, 8 pages
http://dx.doi.org/10.5402/2011/953124
Research Article

On Hyperideals in Left Almost Semihypergroups

Department of Mathematics & Computer Science, Faculty of Natural Sciences, University of Gjirokastra, Gjirokastra 6001, Albania

Received 7 June 2011; Accepted 11 July 2011

Academic Editors: A. V. Kelarev and A. Kiliçman

Copyright © 2011 Kostaq Hila and Jani Dine. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with a class of algebraic hyperstructures called left almost semihypergroups (LA-semihypergroups), which are a generalization of LA-semigroups and semihypergroups. We introduce the notion of LA-semihypergroup, the related notions of hyperideal, bi-hyperideal, and some properties of them are investigated. It is a useful nonassociative algebraic hyperstructure, midway between a hypergroupoid and a commutative hypersemigroup, with wide applications in the theory of flocks, and so forth. We define the topological space and study the topological structure of LA-semihypergroups using hyperideal theory. The topological spaces formation guarantee for the preservation of finite intersection and arbitrary union between the set of hyperideals and the open subsets of resultant topologies.