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==Galois Theory==

==Galois Theory==

The Galois group associated to the nth cyclotomic polynomial is <math>(\mathbb{Z}/n\mathbb{Z})^*</math>, the group of cyclic units modulo n. Cyclotomic fields play an important part in [[algebraic number theory]] and can be used to show that certain constructions posited by ancient Greek geometers are impossible, such as trisecting the angle and constructing certain regular polygons.

The [[Galois group]] associated to the nth cyclotomic polynomial is <math>(\mathbb{Z}/n\mathbb{Z})^*</math>, the group of cyclic units modulo n. Cyclotomic fields play an important part in [[algebraic number theory]] and can be used to show that certain constructions posited by ancient Greek geometers are impossible, such as trisecting the angle and constructing certain regular polygons.

[[Category:Mathematics]]

[[Category:Mathematics]]

[[category:algebra]]

[[category:algebra]]