## Mathematics, Department of

#### Date of this Version

1944

#### Abstract

Let *k* be an algebraic number field of finite degree *m* and let *A* be a normal simple algebra of degree *n*, order *n*^{2}, over *k*. Our object is to prove the following theorem.

**THEOREM.** If *A* is an *R*-algebra, that is, if *n*>2 or at least one infinite prime place of *k* is unramified in *A* when *n*=2, then any two distinct maximal orders of *A* have distinct groups of units.

## Comments

Published in

Bull. Amer. Math. Soc.50 (1944) 405-411.