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Rings with Commuting Nilpotents and Zero Divisors

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Abstract.

We explore the consequences of certain commutativity hypotheses on a single nilpotent element or the set N of all nilpotent elements. We give several sufficient conditions for N to be an ideal. We present some nontrivial examples, including an example in which N is commutative (in fact, N 2 = {0}) and N is not an ideal.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, IL-69978, Tel Aviv, Israel

    Abraham A. Klein

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

    Howard E. Bell

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  1. Abraham A. Klein
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  2. Howard E. Bell
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Correspondence to Abraham A. Klein.

Additional information

Prof. Bell’s research is supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. 3961.

Received: April 27, 2006. Revised: July 31, 2006.

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Klein, A.A., Bell, H.E. Rings with Commuting Nilpotents and Zero Divisors. Result. Math. 51, 73–85 (2007). https://doi.org/10.1007/s00025-007-0259-z

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  • DOI: https://doi.org/10.1007/s00025-007-0259-z

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