| Title | Maximal commutative subrings and simplicity of Ore extensions |
| Authors | Johan Öinert, Johan Richter, Sergei Silvestrov |
| Alternative Location | http://arxiv.org/abs/1111.1292 |
| Alternative Location | http://dx.doi.org/10.1142/S..., Restricted Access |
| Publication | Journal of Algebra and Its Applications |
| Year | 2013 |
| Volume | 12 |
| Issue | 4 |
| Pages | 1250192-1 - 1250192-16 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | World Scientific |
| Abstract English | The aim of this article is to describe necessary and sufficient conditions for simplicity of Ore extension rings, with an emphasis on differential polynomial rings. We show that a differential polynomial ring, Rx;id_R,\delta, is simple if and only if its center is a field and R is \delta-simple. When R is commutative we note that the centralizer of R in Rx;\sigma,\delta is a maximal commutative subring containing $R$ and, in the case when \sigma=id_R, we show that it intersects every non-zero ideal of Rx;id_R,\delta non-trivially. Using this we show that if R is \delta-simple and maximal commutative in Rx;id_R,\delta, then Rx;id_R,\delta is simple. We also show that under some conditions on R the converse holds. |
| Keywords | Ore extension rings, maximal commutativity, ideals, simplicity, |
| ISBN/ISSN/Other | ISSN: 0219-4988 (print) |
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Last update: 2013-04-11
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