Binomial ring
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
2020 Mathematics Subject Classification: Primary: 13F [MSN][ZBL]
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 operations are all equal to the identity.
References
- Yau, Donald Lambda-rings World Scientific (2010) ISBN 978-981-4299-09-1 Zbl 1198.13003
How to Cite This Entry:
Binomial ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Binomial_ring&oldid=54558
Binomial ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Binomial_ring&oldid=54558