Abstract

In analogy to the elementwise definitions of UU- and UJ-rings, a ring R is called UNJ if 1+N(R)+J(R)=U(R). After presenting several characterizations and properties, we consider the UNJ-rings within many well-studied classes of rings. In particular, we examine Dedekind finite rings, 2-primal rings, (semi)regular rings, π-regular rings and rings that satisfy the identity x2=x. Finally, we conclude this paper with group UNJ-rings.