Buckley, Stephen M. and MacHale, Desmond
(2013)
Polynomials That Force a Unital Ring to be Commutative.
Results in Mathematics, 64 (12).
pp. 5965.
ISSN 14226383
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.
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