Abel's Lemma

The pure equation


of prime degree p is irreducible over a field when C is a number of the field but not the pth power of an element of the field.

Jeffreys and Jeffreys (1988) use the term "Abel's lemma" for another lemma related to Abel's uniform convergence test.

See also

Abel's Irreducibility Theorem, Gauss's Polynomial Theorem, Kronecker's Polynomial Theorem, Schönemann's Theorem

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Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 118, 1965.Jeffreys, H. and Jeffreys, B. S. "Abel's Lemma." §1.1153 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 41-42, 1988.

Referenced on Wolfram|Alpha

Abel's Lemma

Cite this as:

Weisstein, Eric W. "Abel's Lemma." From MathWorld--A Wolfram Web Resource.

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