a-Pseudo complementation on ADL’s

Abstract

In this paper, we introduce the concept of an [Formula: see text]-pseudo complementation [Formula: see text] on an Almost Distributive Lattice [Formula: see text] for an arbitrary fixed element [Formula: see text] and any [Formula: see text] of [Formula: see text] and discuss several properties of this. Here, we obtain a bijection correspondence between the [Formula: see text]-pseudo complementations on [Formula: see text] and maximal elements of [Formula: see text] We prove that the set [Formula: see text] is a Boolean algebra which is independent(upto isomorphism) of the [Formula: see text]-pseudo complementation [Formula: see text].

a-minimal prime ideals in almost distributive lattices

“…The class of ADLs with pseudocomplementation was introduced in [8] and proved it is equationally definable. In [5], we introduced the notion of a-pseudo-complementation on an ADL A by fixing an arbitrary element a in A as the natural generalization of the notion of pseudo-complementation on an ADL. In [4], we introduced the concepts of a-dense element and a-maximal filter in an ADL A and studied these in connection with a-pseudocomplementation on A.…”