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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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:	Publisher

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