FILTERS IN ORDERED Gamma-SEMIGROUPS

In this paper we characterize the principal filters on any ordered Gamma-semigroup M and their structure and properties are investigated by using the relation N which is the smallest complete semilattice congruence on M. In particular, we prove that every principal filter of any ordered Gamma-semigroup M can be uniquely determined by its N-classes of M. Also, by using the relation A we will observe that N on any ordered Gamma-semigroup M is the equality relation on M if and only if M is a semilattice such that a <= a gamma a for all a is an element of M, gamma is an element of Gamma, and N is the universal relation on M if and only if M is the only principal filter. We also investigate properties of the complete semilattice congruence classes of M.