Weak GE-Morphisms and Qualified GE-Algebras

Abstract

The notions of weak GE-morphism, weak GE-endomorphism are introduced and investigated its properties. Conditions for a self-map on a GE-algebra to be an idempotent and to be a weak GE-endomorphism are provided. The notion of qualified GE-algebra is introduced and its properties are investigated. Condition for a qualified GE-algebra to be an idempotent weak GE-endomorphism is given. The notion of qualified self-map is defined and a necessary and condition for a given self-map on a GE-algebra, the product of two GE-algebras under the qualified self-map to be a qualified GE-algebra is given. For a given qualified GE-algebra, using its kernel, an equivalence relation is induced, and then the quotient set is constructed. A binary operation is given on the quotient set to create a quotient qualified GE-algebra.