In abstract algebra, a rupture field of a polynomial over a given field is a field extension generated by a root.

.

is irreducible are isomorphic, then the ring homomorphism is an isomorphism. Also, in this case the degree of the extension equals the degree.

does not contain the other two (complex is a primitive cube root of unity). For a field containing all the roots of a polynomial, see Splitting field.

Examples

. It is also a splitting field.

which squares (and all quadratic extensions).

References