The Irrationality of Sums of Radicals via Cogalois Theory
نویسنده
چکیده
In this paper we present an one-and-a-half-line proof, involving Cogalois Theory, of a folklore result asking when is an irrational number a sum of radicals of positive rational numbers. Some of the main ingredients of Cogalois Theory like G-Kneser extension, G-Cogalois extension, etc., used in the proof are briefly explained, so that the paper is selfcontained. We also discuss some older and newer results on transcendental and irrational numbers.
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