Properties of K-Isomorphism on K-Algebra

Abstract

K-Algebra is a system that is built on a group with unit element (G, *) and binary operation , that defined and satisfies certain axioms. Let and are K-Algebra. K-Homomorphism on K-Algebra that is a mapping from K1-Algebra to K2-Algebra that satisfies . Based on the result, K-Isomorphism on K-Algebra is µ that satisfies bijective function. By adopting a concept of isomorphism group, it has been proven that some concepts such as theorems and propositions also apply on K-Ismorphism on K-Algebra. If is K-Isomorphism, then also K-Isomorphism. Then, apply µ(e1) = e2, and and n ∈ Z+. Order of any element in K-Algebra that is positive integer n, so that gn = e.