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 .