# Binomial ring

In mathematics, a **binomial ring** is a commutative ring whose additive group is torsion-free and contains all binomial coefficients

for *x* in the ring and *n* a positive integer. Binomial rings were introduced by Hall (1969).

Elliott (2006) showed that binomial rings are essentially the same as λ-rings for which all Adams operations are the identity.

## References

- Elliott, Jesse (2006), "Binomial rings, integer-valued polynomials, and λ-rings",
*Journal of Pure and Applied Algebra*,**207**(1): 165–185, doi:10.1016/j.jpaa.2005.09.003, ISSN 0022-4049, MR 2244389 - Hall, Philip (1969) [1957],
*The Edmonton notes on nilpotent groups. Notes of lectures given at the Canadian Mathematical Congress Summer Seminar (University of Alberta, 12–30 august 1957)*, Queen Mary College Mathematics Notes, Mathematics Department, Queen Mary College, London, ISBN 978-0-902480-06-3, MR 0283083 - Yau, Donald (2010),
*Lambda-rings*, Hackensack, NJ: World Scientific Publishing Co. Pte. Ltd., ISBN 978-981-4299-09-1, MR 2649360

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