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,
See also Abel's Lemma, Kronecker's Polynomial Theorem, Schoenemann's Theorem
References
Abel, N. H. ``Mémoire sur une classe particulière d'équations résolubles algébriquement.'' J. reine angew. Math. 4, 1829.
Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 120, 1965.