Forceable weak eGE-algebras and quotient GE-algebras

Abstract

The concept of forceable weak eGE-algebras is introduced, and its associated properties are investigated. The structure of GE-filters in the GE-algebras derived from weak eGE-algebras is discussed. The relationship between an eGE-algebra and a forceable weak eGE-algebra is considered, and the characterization of an eGE-filter in weak eGE-algebras is established. Using eGE-filter in forceable weak eGE-algebras, 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 GE-algebra, and an example is given to illustrate it.