A study of soft hyperideals in right regular LA-semihypergroups

Abstract

Although a lot of work has been done by algebraist on soft set theory and hyperstructure theory, several fundamental results of soft intersection hyperideals in LA-semihypergroups remained untouched. This paper aims at studying some structural properties of LA-semihypergroups by applying soft set theory. In this paper, we define right regular LA-semihypergroups and introduce the concept of soft generalized bi-hyperideals in LA-semihypergroups. Further, we characterize right regular LA-semihypergroups in terms of different kinds of soft right hyperideals, soft left hyperideals and soft generalized bi-hyperideals. Idempotent soft hyperideals in LA-semihypergroups are introduced and some related results on them are obtained. It is proved that in an LA-semihypergroup with left identity, the collection of all soft left hyperideals, which are idempotent forms a commutative monoid. Examples are provided to illustrate the results.