The pure equation
of prime degree 
is irreducible over a field when
is a number of the field
but not the 
th
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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References
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. https://mathworld.wolfram.com/AbelsLemma.html
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