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    Polynomials That Force a Unital Ring to be Commutative


    Buckley, Stephen M. and MacHale, Desmond (2013) Polynomials That Force a Unital Ring to be Commutative. Results in Mathematics, 64 (1-2). pp. 59-65. ISSN 1422-6383

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    Official URL: http://link.springer.com/article/10.1007%2Fs00025-...


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    Abstract

    We characterize polynomials f with integer coefficients such that a ring with unity R is necessarily commutative if f(R) = 0, in the sense that f(x) = 0 for all x∈R . Such a polynomial must be primitive, and for primitive polynomials the condition f(R) = 0 forces R to have nonzero characteristic. The task is then reduced to considering rings of prime power characteristic and the main step towards the full characterization is a characterization of polynomials f such that R is necessarily commutative if f(R) = 0 and R is a unital ring of characteristic some power of a fixed prime p.

    Item Type: Article
    Keywords: 16R50; Unital ring; Polynomial identity; Commutativity; Monoid ring;
    Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 4829
    Identification Number: https://doi.org/10.1007/s00025-012-0296-0
    Depositing User: Prof. Stephen Buckley
    Date Deposited: 18 Mar 2014 12:15
    Journal or Publication Title: Results in Mathematics
    Publisher: Springer Verlag (Germany)
    Refereed: Yes
    URI:

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