Alpha Ideals and the Space of Prime Alpha Ideals in Universal Algebras

Abstract

The purpose of this paper is to study $\alpha$ -ideals in a more general context, in universal algebras having a constant $0$ . Several characterizations are obtained for an ideal $I$ of an algebra $A$ to be an $\alpha$ -ideal. It is shown that the class of all $\alpha$ -ideals of an algebra $A$ forms an algebraic lattice. Prime $\alpha$ -ideals and several related properties are investigated. Some properties of the spectral space of prime $\alpha$ -ideals equipped with the hull-kernel topology are derived.