Congruence Relations On Almost Distributive Lattices

Abstract

This thesis aims to develop a better understanding of Almost Distributive Lattices and it’s congruence relations. We present the definition of Almost Distributive Lattice, and state important properties of an ADL that will be used in developing further theory, we also introduce the concept of congruence relations, and discuss special congruence relations in an ADL. Furthermore we discuss the notion of derivation in an ADL and it’s properties, then two kinds of congruence are proposed in an ADL. Also, we introduced the concept of Regular ring and study spacial congruence on it. Finally, we introduce the concept of θ− filters and θ− ideals in an ADL and characterized them in terms of ADL congruence.