International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 2, Pages 237-245
On generalized quaternion algebras
Department of Mathematics, Bradley University, Peoria 61625, Illinois, USA
Received 1 February 1979; Revised 13 July 1979
Copyright © 1980 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.
Let be a commutative ring with , and an automorphism group of of order . The generalized quaternion ring extension over is defined by . Parimala and . Sridharan such that (1) is a free -module with a basis , and (2) and for each in . The purpose of this paper is to study the separability of . The separable extension of over is characterized in terms of the trace of over the subring of fixed elements under . Also, the characterization of a Galois extension of a commutative ring given by Parimala and Sridharan is improved.