Author: A. Chin 1
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  • 1 University of Malaya Institute of Mathematical Sciences, Faculty of Science 50603 Kuala Lumpur Malaysia 50603 Kuala Lumpur Malaysia
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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 xR, there exist a positive integer n and an element yR such that x n=x n +1 y and xy=yx. R is said to be periodic if for each xR there are integers m,n≥ 1 such that mn 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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