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Buckley, Stephen M. and MacHale, D. (2012) Centrifiers and ring commutativity. Journal of Mathematical Sciences: Advances and Applications, 15. pp. 139-161. ISSN 0974-5750
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Abstract
A result of Herstein says in particular that if there exists n > 1
such that xᵑ − x ∈ Z(R) for all x in a ring R then R is commutative. We give an elementary proof of this fact for certain values of n, based on the theory of centrifiers which we develop. For n = 5; 7, we also give an elementary proof of the
commutativity of rings R such that xᵑ + x ∈ Z(R) for all x ∈ R.
| Item Type: | Article |
|---|---|
| Additional Information: | This is the preprint version of the published article. |
| Keywords: | Centrifiers; ring commutativity; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 6983 |
| Depositing User: | Prof. Stephen Buckley |
| Date Deposited: | 23 Feb 2016 12:56 |
| Journal or Publication Title: | Journal of Mathematical Sciences: Advances and Applications |
| Publisher: | Scientific Advances Publishers |
| Refereed: | Yes |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/6983 |
| 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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