On two questions of Nicholson

Year 2022, , 90 - 99, 17.01.2022

Feroz Sıddıque

https://doi.org/10.24330/ieja.1058418

Abstract

We show that a ring $R$ has stable range one if and only if every
left unit lifts modulo every left principal ideal. We also show
that a left quasi-morphic ring has stable range one if and only if
it is left uniquely generated. Thus we answer in the affirmative
the two questions raised by W. K. Nicholson.

Keywords

Directly-finite ring, stable range one, left quasi-morphic ring

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