Generalized Birkhoff Center of Almost Distributive Lattices

Abstract

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.

MSC-2010: 06D99

Key words: Birkhoff center of ADLs; Sectional Birkhoff center of ADLs; generalized Birkhoff center of ADLs.