Difference between revisions of "Binomial ring"
From Encyclopedia of Mathematics
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| − | * Yau, Donald ''Lambda-rings'' World Scientific (2010) ISBN 978-981-4299-09-1 {{ZBL|1198.13003}} | + | * Yau, Donald ''Lambda-rings'' World Scientific (2010) {{ISBN|978-981-4299-09-1}} {{ZBL|1198.13003}} |
Latest revision as of 20:19, 20 November 2023
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=39491
Binomial ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Binomial_ring&oldid=39491