On Quasi-P-Almost Distributive Lattices.
- Resource Type
- Article
- Authors
- Bandaru, Ravi Kumar; Rao, G.C.
- Source
- Discussiones Mathematicae: General Algebra & Applications. Jun2020, Vol. 40 Issue 1, p5-19. 15p.
- Subject
- *BOOLEAN algebra
*DISTRIBUTIVE lattices
*IDEALS (Algebra)
*KERNEL (Mathematics)
*GENERALIZATION
- Language
- ISSN
- 1509-9415
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. [ABSTRACT FROM AUTHOR]