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    Variations on a Theme: Rings Satisfying x³ = x Are Commutative


    Buckley, S.M. and MacHale, D. (2013) Variations on a Theme: Rings Satisfying x³ = x Are Commutative. American Mathematical Monthly, 120 (5). pp. 430-440. ISSN 0002-9890

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    Abstract

    A ring satisfying x³ = x is necessarily commutative. We consider a variety of weaker forms of this condition and show that many but not all of them imply commutativity. We also present a variety of elementary proofs of the fact that x³ = x implies commutativity.

    Item Type: Article
    Additional Information: This is the preprint version of the published article, which is available at DOI: 10.4169/amer.math.monthly.120.05.430
    Keywords: Rings; Commutative;
    Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 6982
    Identification Number: https://doi.org/10.4169/amer.math.monthly.120.05.430
    Depositing User: Prof. Stephen Buckley
    Date Deposited: 23 Feb 2016 12:25
    Journal or Publication Title: American Mathematical Monthly
    Publisher: Mathematical Association of America
    Refereed: Yes
    URI:

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