Remarks on the group of unıts of a corner ring

Year 2021, Volume: 42 Issue: 2, 321 - 326, 30.06.2021

Tülay Yıldırım

https://doi.org/10.17776/csj.745918

Abstract

The aim of this study is to characterize rings having the following properties for a non-trivial idempotent element e of R, U (eRe) = e + eJ(R)e = e + J (eRe) (and U (eRe) = e + N (eRe)),
where U (-), N (-) and J (-) denote the group of units, the set of all nilpotent elements and the Jacobson radical of R, respectively. In the present paper, some characterizations are also obtained in terms of every element is of the form e + u, where e2 = e ∈ R and u ∈ U(eRe).

Keywords

UJ rings, Corner rings, Clean elements, Lifting idempotents

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