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The purpose of this paper is to study α-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 α-ideal. It is shown that the class of all α-ideals of an algebra A forms an algebraic lattice. Prime α-ideals and several related properties are investigated. Some properties of the spectral space of prime α-ideals equipped with the hull-kernel topology are derived.