sambasiva rao mukkamala

The concepts of regular filters and π--filters are introduced in distributive lattices. A set of equivalent conditions is given for a D-filter to become a regular filter. For every D-filter, it is proved that there exists a homomorphism whose dense kernel is a regular filter. π--filters are characterized in terms of regular filters and congruences. Some equivalent conditions are given for the space of all prime π-filters to become a Hausdorff space.

Properties of prime filters and maximal filters of transitive GE-algebras are investigated. An element-wise characterization is derived for the smallest GE-filter containing a given set. It is proved that the set of all GE-filters of a transitive GE-algebra forms a complete distributive lattice. Four different versions of a prime filter theorem are generalized in transitive GE-algebras. A necessary and sufficient condition is derived for a proper filter of a commutative GE-algebra to become a prime filter.

The concepts of intrinsic ideals and inlets are introduced in a distributive lattice. Intrinsic ideals are also characterized with the help of inlets. Certain equivalent conditions are given for an ideal of a distributive lattice to become intrinsic. Some equivalent conditions are derived for the quotient lattice, with respect to a congruence, to become a Boolean algebra. Some topological properties of the prime spectrum of intrinsic ideals of distributive lattice are derived.