 For example, the only finite field extension of the real numbers is the complex numbers, while the quaternions are a central simple algebra over the reals, and all CSAs over the reals are Brauer equivalent to the reals or the quaternions.CSAs can be further generalized to Azumaya algebras, where the base field is replaced by a commutative local ring.Given a field extension, one can "extend scalars" on associated algebraic objects.