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Weakly UU rings. (English) Zbl 1377.16031

A ring \(R\) is called 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 T.-Y. Lam) [Publ. Math. 88, No. 3–4, 449–466 (2016; Zbl 1374.16089)], to this new point of view.

MSC:

16U60 Units, groups of units (associative rings and algebras)
16N40 Nil and nilpotent radicals, sets, ideals, associative rings
16N20 Jacobson radical, quasimultiplication

Citations:

Zbl 1374.16089
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