International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 703-709
On free ring extensions of degree
Mathematics Department, Bradley University, Peoria 61625, Illinois, USA
Received 25 June 1980
Copyright © 1981 George Szeto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Nagahara and Kishimoto  studied free ring extensions of degree for some integer over a ring with 1, where , for all and some in , and is a basis. Parimala and Sridharan , and the author investigated a class of free ring extensions called generalized quaternion algebras in which and is of order 2. The purpose of the present paper is to generalize a characterization of a generalized quaternion algebra to a free ring extension of degree in terms of the Azumaya algebra. Also, it is shown that a one-to-one correspondence between the set of invariant ideals of under and the set of ideals of leads to a relation of the Galois extension over an invariant subring under to the center of .