Elitable GE-filters of bordered GE-algebras

Abstract

In this paper, the notions of maximal GE-filter and prime GE-filter of a GE-algebra are introduced and the relation between them is given. Some characterizations of prime GE-filters of a transitive GE-algebra are given in terms of the GE-filter generated by a subset of a transitive GE-algebra. We generalized Stone's theorem to transitive GE-algebras. The notion of elitable GE-filter of a bordered GE-algebra is introduced and investigated its properties. We observed that the class of all elitable GE-filters of a transitive bordered GE-algebra is a complete distributive lattice. Equivalent conditions for a GE-filter of a transitive bordered GE-algebra to be elitable GE-filter are given. We provided conditions for a subset of a transitive bordered GE-algebra to be elitable GE-filter.