Abel's irreducibility theorem


In mathematics, Abel's irreducibility theorem, a field theory result described in 1829 by Niels Henrik Abel, asserts that if ƒ is a polynomial over a field F that shares a root with a polynomial g that is irreducible over F, then every root of g is a root of ƒ. Equivalently, if ƒ shares at least one root with g then ƒ is divisible evenly by g, meaning that ƒ can be factored as gh with h also having coefficients in F.
Corollaries of the theorem include: