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# The Structure of Alternative Division Rings.

@article{Bruck1951TheSO, title={The Structure of Alternative Division Rings.}, author={R H Bruck and Erwin Kleinfeld}, journal={Proceedings of the National Academy of Sciences of the United States of America}, year={1951}, volume={37 2}, pages={88-90} }

- Published 1951 in Proceedings of the National Academy of Sciences…

1. Introduction. A ring R is said to be alternative if (xx)y = x(xy), (yx)x=y(xx) for all x, y of R. And R is a division ring if it has a non-zero element and the equations ax = b, ya = b have unique solutions x, y for a ^0; the existence of a unit is not postulated. Let R be an alternative ring without divisors of zero.1 If a, b are nonzero elements of R and m is a rational integer, the equation (na)b = a(nb) shows that na = 0 if and only if nb = 0. Therefore we can assign a characteristic… CONTINUE READING

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