Closure Operators on Complete Almost Distributive Lattices-III

Calyampudi Radhakrishna Rao; Venugopalam Undurthi

doi:10.18778/0138-0680.44.1.2.08

Authors

Calyampudi Radhakrishna Rao Department of Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh, India - 530003
Venugopalam Undurthi Department of Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh, India - 530003

DOI:

https://doi.org/10.18778/0138-0680.44.1.2.08

Keywords:

Complete Almost Distributive Lattice, Closure operator, Dual atom, Dual atomistic, Completely meet-irreducible element

Abstract

In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meet-irreducible element in a complete ADL and derive a necessary and sufficient condition for a dual atom of Φ (L) to be complemented.

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