Weakly UU rings (Q329130)

A ring \(R\) is called \textsl{weakly} UU, and abbreviated as WUU, if \( U(R)=\mathrm{Nil}(R)\pm 1\). This is equivalent to the condition that every unit can be presented as either \(t+1\) or \(t-1\), where \(t\in \mathrm{Nil}(R)\). The objective of this article is to generalize considerably almost all results from the previous joint paper (with \textit{T.-Y. Lam}) [Publ. Math. 88, No. 3--4, 449--466 (2016; Zbl 1374.16089)], to this new point of view.