On rings whose Jacobson radical coincides with upper nilradical

Abstract

We call a ring R is JN if whose Jacobson radical coincides with upper nilradical, and R is right SR if eachelement r ∈ R can be written as r = s+r where s is an element from the right socle and r is a regular element of R. SRrings is a class of special subrings of JN rings, which is the extension of soclean rings. We give their some characterizationsand examples, and investigate the relationship between JN rings, SR rings and related rings, respectively.