## Future high-school math teachers and upper-level math courses

- R. O. Hill
- Notices Amer. Math. Soc
- 2005

@article{Waterhouse2012SquareRA, title={Square Root as a Homomorphism}, author={William C. Waterhouse}, journal={The American Mathematical Monthly}, year={2012}, volume={119}, pages={235-239} }

- Published 2012 in The American Mathematical Monthly
DOI:10.4169/amer.math.monthly.119.03.235

In any field K where−1 is not a square, there are homomorphisms from the squares to (chosen) square roots in K . Maximal fields F with such homomorphisms have Gal(F̄/F) either Z/2Z or the 2-adic integers. By and large, high school algebra students (thinking of positive real numbers) learn that √ cd = √ c · √ d . Most mathematicians know that there is no way of making this work for complex numbers. The most common account of this (see [3], for instance) seems to focus on how a square root… CONTINUE READING

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