Cyclic algebra

In algebra, a cyclic division algebra is one of the basic examples of a division algebra over a field, and plays a key role in the theory of central simple algebras.
Definition.
Let "A" be a finite-dimensional central simple algebra over a field "F". Then "A" is said to be cyclic if it contains a strictly maximal subfield "E" such that "E"/"F" is a cyclic field extension (i.e., the Galois group is a cyclic group).