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On Commutativity of Semiperiodic Rings

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Abstract.

Let R be a ring with center Z, Jacobson radical J, and set N of all nilpotent elements. Call R semiperiodic if for each \(x \in R\setminus(J\cup Z)\), there exist positive integers m, n of opposite parity such that \(x^n - x^m \in N\). We investigate commutativity of semiperiodic rings, and we provide noncommutative examples.

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Authors and Affiliations

  1. Department of Mathematics, Brock University, St. Catharines, Ontario, L2S 3A1, Canada

    Howard E. Bell

  2. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA

    Adil Yaqub

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  1. Howard E. Bell
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  2. Adil Yaqub
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Correspondence to Howard E. Bell.

Additional information

Received: March 7, 2008.

Prof. Bell’s research was supported by the Natural Sciences and Engineering Research Council of Canada, Grant 3961.

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Bell, H.E., Yaqub, A. On Commutativity of Semiperiodic Rings. Result. Math. 53, 19–26 (2009). https://doi.org/10.1007/s00025-008-0305-5

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  • DOI: https://doi.org/10.1007/s00025-008-0305-5

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