Every Finite Division Ring is a Field

David Johnston

Friday 22nd January, 2010 16:00-17:00 Mathematics Building, room 515


It is easy to think of a non-commutative division ring: the quaternions. However, as the title suggests, we can prove that any non-commutative division ring must necessarily be infinite. Many mathematicians (Artin, Bourbaki, Wedderburn and others) have given proofs of this remarkable theorem. We present a particularly elegant offering given by Ernst Witt in 1931. Only elementary ideas are needed: thus, the only prerequisites are linear algebra, ultra basic group theory and familiarity with complex roots of unity. Briefly perusing the class formula may be advantageous.

Add to your calendar

Download event information as iCalendar file (only this event)