Abel,s Irreducibility Theorem
المؤلف:
Dörrie, H
المصدر:
100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover
الجزء والصفحة:
1258
Abel's Irreducibility Theorem
If one root of the equation 
, which is irreducible over a field 
, is also a root of the equation 
in 
, then all the roots of the irreducible equation 
are roots of 
. Equivalently, 
can be divided by 
without a remainder,
where 
is also a polynomial over 
.
REFERENCES:
Abel, N. H. "Mémoire sur une classe particulière d'équations résolubles algébriquement." J. reine angew. Math. 4, 131-156, 1829. Reprinted as Ch. 25 in Abel, N. H. Oeuvres complètes, tome 1. J. Gabay, pp. 478-507, 1992.
Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 120, 1965.
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