A note on strongly π-regular rings |
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Authors: | A. Y. M. Chin |
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Affiliation: | (1) Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia |
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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. This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | periodic nilpotent Jacobson radical idempotent regular strongly ?-regular |
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