GE-ALGEBRAS WITH NORMS

Abstract

In this paper, we introduce and study the concept of normed GE-algebras, an extension of GE-algebras equipped with a GE-norm, which provides a framework to measure the magnitude of algebraic elements. We define the magnitude function and explore its properties in the context of GE-algebras. Through theorems and propositions, we examine the behavior of sequences in these normed structures, demonstrating convergence properties, quasi-metrics, and the relationship between norms and algebraic operations. We also establish the connection between normed GE-algebras and their product spaces, as well as the implications for convergent sequences and limit uniqueness. Finally, we generalize these results to mappings between normed GE-algebras and investigate the implications of GE-morphisms in preserving convergence behavior.