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.
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/s0002501202960 
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: 

Use Licence: 
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BYNCSA). Details of this licence are available
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