On two questions of Nicholson

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International Electronic Journal of Algebra
Volume:31 Issue:31
On two questions of Nicholson

On two questions of Nicholson

Pages : 90-99

View : 114 | Download : 5

Publication Date : 2022-01-17

Article Type : Research Paper

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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