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.

Keywords

• $\alpha$-seminearring
• strictly-$\alpha$ seminearring
• distributively generated seminearring
• mate function
• ideal

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