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Square Root as a Homomorphism

William C. Waterhouse
The American Mathematical Monthly
Vol. 119, No. 3 (March 2012), pp. 235-239
DOI: 10.4169/amer.math.monthly.119.03.235
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.119.03.235
Page Count: 5
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Square Root as a Homomorphism
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Abstract

Abstract 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(F/F) either ℤ/2ℤ or the 2-adic integers.

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