View source for Binomial ring

{{TEX|done}}{{MSC|13F}}

A ring $R$ with torsion-free addition in which all binomial symbols
$$
\binom{x}{n} = \frac{x(x-1)\cdots(x-n+1)}{n!}
$$
are well-defined as functions on $R$: the corresponding elements of $R \otimes_{\mathbf{Z}} \mathbf{Q}$ lie in $R$.  Clearly any field of characteristic zero is a binomial ring, as is the ring of integers $\mathbf{Z}$.

If $R$ is binomial, then defining $\lambda^n (a) = \binom{a}{n}$ makes $R$ a [[lambda-ring]] with operators $\lambda^n$.  The [[Adams operation]]s are all equal to the identity.

====References====
* Yau, Donald ''Lambda-rings'' World Scientific (2010) ISBN 978-981-4299-09-1 {{ZBL|1198.13003}}