of BE-algebras. In particular we define the proper
notion of ideal for this class of algebras. After introducing the notions of transitive and
self distributive BE-algebras as rather natural subclasses of interest in terms of an order
relation associated with the product-operation of the algebras of this type, we obtain several
characterizations of ideals in this setting as unions of special collections of upper sets A(x, y)
(defined below) in these algebras.