Algebraic Structure of Supernilpotent Radical Class Constructed from a Topology Thychonoff Space

Abstract

A radical class of rings is called a supernilpotent radicals if it is hereditary and it contains the class for some positive integer In this paper, we start by exploring the concept of Tychonoff space to build a supernilpotent radical. Let be a Tychonoff space that does not contain any isolated point. The set of all continuous real-valued functions defined on is a prime essential ring. Finally, we can show that the class of rings is a supernilpotent radical class containing the matrix ring .