Generalized Birkhoff Center of Almost Distributive Lattices
Berhanu Assaye Alaba, Mihret Alamneh Taye, Gezahagne Mulat Addis · Annals of Pure and Applied Mathematics · 2019
In this paper we define sectional Birkhoff center for an Almost Distributive Lattice not necessarily with maximal elements; as a Birkhoff center of its principal ideals.Moreover, we extend this result and define the generalized Birkhoff center of an ADL not necessarily with maximal elements.We give a necessary and sufficient condition for an ADL to be relatively complemented in terms of its sectional Birkhoff centers.Also we define and characterize sectionaly complemented ideals and sectional factor congruences using sectional Birkhoff centers