Extended GE-filters in weak eGE-algebras

Abstract

A broader concept than eGE algebra, called weak eGE algebra, is introduced, and related properties are studied. The concept of transitive and tightly (weak) eGE algebra is also considered and some properties are discussed. A weak eGE-algebra with additional conditions is used to give a way to create a GE-algebra. Extended GE filters are described in the last section. The concept of eGE-filters and upper sets is introduced and associated properties are investigated. Conditions for a superset of E in a weak eGE-algebra (X, *, E) to be an eGE-filter are provided. Also, conditions for the upper set to become an eGE-filter are discussed. The characterization of the eGE-filter is established.