Soft Sub-nearsemirings, Soft Ideals and Soft S-Subsemigroups of Nearsemirings

Abstract

In this note, we introduce and discuss the notions of soft sub-nearsemirings, soft ideals and soft S-subsemigroups of nearsemirings. Some related properties and characterizations of these soft algebraic structures are discussed with illustrative examples. For the sake of investigations, we apply several operations of soft sets including soft intersection sum, soft product and soft uniint product. Based on these operations, we also discuss few characterizations of distributively generated nearsemirings. In due course, we investigate few relationships among these soft algebraic structures and the classical nearsemirings. We also introduce the notion of soft ideals (left and right) of nearsemirings. Firstly, we investigate these ideals by applying few operations on them. Then, we present the relationship between these soft ideals of nearsemiring with the classical ideals of nearsemirings. Moreover, we introduce the notion of soft S-homomorphism between two soft S-subsemigroups and investigate that the homomorphic image of soft S-subsemigroup is a soft S-subsemigroup. Throughout, we shift several substructures of nearsemirings towards the soft algebraic substructures of nearsemirings by utilizing different algebraic methods. Consequently, we explore a linkage among the soft set theory, classical set theory and nearsemiring theory. Mainly, our study is the interplay between soft substructures of nearsemirings and classical substructures of nearsemirings.