Abstract
Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that x n=x n +1 y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and x m=x n. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained.
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Chin, A.Y.M. A note on strongly π-regular rings. Acta Mathematica Hungarica 102, 337–342 (2004). https://doi.org/10.1023/B:AMHU.0000024683.13344.cf
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DOI: https://doi.org/10.1023/B:AMHU.0000024683.13344.cf