International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 4, Pages 779-784
On separable abelian extensions of rings
Mathematics Department, Bradley University, Peoria 61625, Illinois, USA
Received 9 February 1982
Copyright © 1982 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 ring with , a finite abelian automorphism group of of order where is cyclic of order . for some integers , , and , and the center of whose automorphism group induced by is isomorphic with . Then an abelian extension is defined as a generalization of cyclic extensions of rings, and is an Azumaya algebra over such that if and only if is Galois over with Galois group (the Kanzaki hypothesis).