The sum-product phenomenon in arbitrary rings
| dc.creator | Tao, Terence | |
| dc.date | 2008-06-16 | |
| dc.date | 2009-02-23 | |
| dc.date.accessioned | 2026-07-07T12:44:38Z | |
| dc.date.available | 2026-07-07T12:44:38Z | |
| dc.description | The \emph{sum-product phenomenon} predicts that a finite set $A$ in a ring $R$ should have either a large sumset $A+A$ or large product set $A \cdot A$ unless it is in some sense "close" to a finite subring of $R$. This phenomenon has been analysed intensively for various specific rings, notably the reals $\R$ and cyclic groups $\Z/q\Z$. In this paper we consider the problem in arbitrary rings $R$, which need not be commutative or contain a multiplicative identity. We obtain rigorous formulations of the sum-product phenomenon in such rings in the case when $A$ encounters few zero-divisors of $R$. As applications we recover (and generalise) several sum-product theorems already in the literature. | |
| dc.description | 26 pages, no figures, to appear, Contributions to Discrete Mathematics. Some final corrections | |
| dc.identifier | https://arxiv.org/abs/0806.2497 | |
| dc.identifier | http://arxiv.org/abs/0806.2497 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220836 | |
| dc.subject | Combinatorics | |
| dc.subject | 11B75; 16B99 | |
| dc.title | The sum-product phenomenon in arbitrary rings | |
| dc.type | text |