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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-...
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: | 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 |
| Related URLs: | |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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