Abel's Irreducibility Theorem
If one Root of the equation 
, which is irreducible over a Field 
, is also a Root ofthe 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 .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.
- Catalan's Diophantine Problem
- Catalan Solid
- Catalan's Problem
- Catalan's Surface
- Catalan's Triangle
- Catalan's Trisectrix
- Catastrophe
- Catastrophe Theory
- Categorical Game
- Categorical Variable
- Category
- Category Theory
- Catenary
- Catenary Evolute
- Catenary Involute
- Catenary Radial Curve
- Catenoid
- Caterpillar Graph
- Cat Map
- Cattle Problem of Archimedes
- Cauchy Binomial Theorem
- Cauchy Boundary Conditions
- Cauchy Criterion
- Cauchy Distribution
- Cauchy Equation