Monogenic field

In mathematics, a monogenic field is an algebraic number field K for which there exists an element a such that the ring of integers O_K is the polynomial ring Z[a]. The powers of such an element a constitute a power integral basis.

In a monogenic field K, the field discriminant of K is equal to the discriminant of the minimal polynomial of α.

Examples of monogenic fields include:

While all quadratic fields are monogenic, already among cubic fields there are many that are not monogenic. The first example of a non-monogenic number field that was found is the cubic field generated by a root of the polynomial ${\displaystyle X^{3}-X^{2}-2X-8}$, due to Richard Dedekind.

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