Abstract
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.
Highlights
0-distributive lattices by Pawar and Khopade [2], to the class of almost distributive lattices by Rao and Rao [3], to the class of C-algebras by Rao [4], and more generally to arbitrary posets by Mokbel [5]
It is observed that the map J ⟼ ←αα(J) forms a closure operator on the class of all ideals of L and α−ideals in L are defined to be those ideals which are closed with respect to this closure operator, i.e., J is an α−ideal of L if
In [8], Chajda and Halas have introduced the notion of annihilators in general universal algebras having a constant 0
Summary
0-distributive lattices by Pawar and Khopade [2], to the class of almost distributive lattices by Rao and Rao [3], to the class of C-algebras by Rao [4], and more generally to arbitrary posets by Mokbel [5]. We have studied the basic topological properties of the space of α-prime ideals in universal algebras. In a finite algebra A, every α−ideal is an annihilator ideal. Let A be a c−idempotent algebra and P be a prime ideal of A.
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