VOLUNTARY GE-FILTERS AND FURTHER RESULTS OF GE-FILTERS IN GE-ALGEBRAS

Abstract

Further properties on (belligerent) GE-filters are discussed, and the quotient GE-algebra via a GE-filter is established. Conditions for the set (c) over right arrow to be a belligerent GE-filter are provided. The extension property of belligerent GE-filter is composed. The notions of a balanced element, a balanced GE-filter, an anti- symmetric GE-algebra and a voluntary GE-filter are introduced, and its properties are examined. The relationship between a GEsubalgebra and a GE-filter is established. Conditions for every element in a GE-algebra to be a balanced element are provided. The conditions necessary for a GE-filter to be a voluntary GEfilter are considered. The GE-filter generated by a given subset is established, and its shape is identified.