On Quasi-P-Almost Distributive Lattices

Abstract

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 su cient 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.

Keywords

• pseudo-complementation
• quasi pseudo-complementation
• almost distributive lattice (adl)
• p-adl
• quasi-p-adl
• 06d99
• 06d15