On quasi-p-Almost Distributive Lattices
Ravikumar Bandaru, G. C. Rao · Discussiones Mathematicae - General Algebra and Applications · 2020
In this paper, the concept of quasi pseudo-complementation on an Almost Distributive Lattice (ADL) as a generalization of pseudo-complementation on an ADL is introduced and its properties are studied.Necessary and sufficient conditions for a quasi pseudo-complemented ADL(q-p-ADL) to be a pseudo-complemented ADL(p-ADL) and Stone ADL are derived and the set S(L) = {a * | a ∈ L} is proved to be a Boolean algebra.Also, the notions of * -congruence and kernel ideals are introduced in a quasi-p-ADL and characterized kernel ideals.Finally, some equivalent conditions are given for every ideal of a quasi-p-ADL to be a kernel ideal.