The structure of certain unique classes of seminearrings

Abstract

In this paper, we introduce the classes of $\alpha$ and strictly-$\alpha$ seminearrings and establishes some of their properties, mostly in relation to the possession of a mate function. Then we get the criterion for an $\alpha$-seminearring to become a strictly-$\alpha$ seminearring. We also obtain a complete characterisations of $\alpha$ and strictly-$\alpha$ seminearrings and proved certain results for $\alpha$ and strictly-$\alpha$ seminearrings via certain unique classes of seminearrings.