GE-Morphisms of GE-Algebras

Abstract

In this paper, the notion of GE-morphism is introduced, and established fundamental GE-morphism theorem. We investigated some isomorphism theorems in GE-algebras. We derived that the image of a GE-filter of a given GE-algebra X under GE-epimorphism f : X -> Y is also a GE-filter of a GE-algebra Y. We established the one-to-one correspondence between the GE-filters of a GE-algebra X containing ker(f) and GE-filters of Y whenever f : X -> Y is GE-epimorphism. We introduced the concept of extended GE-morphism(eGE-morphism) in (weak) eGE-algebras and investigated its properties. We provided conditions for the image of superset F-X of E-X is an eGE-filter of f(X) whenever f : (X, (*X), E-X) -> (Y, (*Y) , E-Y) is a GE-morphism.