Abstract:
This thesis aims to develop a better understanding of ideals, congruence relations
and derivations in distributive lattices. We present the definition of a partially
ordered set, a lattice and a distributive lattice, and we furnish the relation between
these concepts. We introduce the concept of ideal, filter, prime ideal and maximal
ideal in lattices . Also we discuss some results related to ideals and their relationship
with distributivity. We introduce the concepts of congruence relations, quotient
lattices and kernels. In addition we characterize the distributive lattices by kernels.
Furthermore we discuss the notion of derivation in lattices and its properties. We
compare between derivations in lattices and lattice homomorphisms. Also we present
the concepts of d-ideal, injective ideal and discuss two types of congruences on a
distributive lattice with respect to derivations . Finally the Stone's result for ideals
of a distributive lattice is extended to the case of injective ideals and d-prime ideals
