Alpha ideals and the space of prime alpha ideals in universal algebras (Q2230030)

Summary: 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.