A Theorem on the Unit Groups of Simple Algebras

Authors

Ralph Hull, University of Nebraska - Lincoln

Document Type

Article

Date of this Version

1944

Comments

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

Abstract

Let k be an algebraic number field of finite degree m and let A be a normal simple algebra of degree n, order n², 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.