Characterizations of ρ-algebra and Generation Permutation Topological ρ-algebra using Permutation in Symmetric Group

The aim of this work is to introduce new branch of the pure algebra it's called algebra. Further, some new concepts like subalgebra, ideal, ideal and permutation topological algebra are introduced and studied. It is pointed out that algebra need not be algebra or algebra by a counterexample. Moreover, several examples are given to illustrate the concepts introduced in this paper.