International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 1, Pages 103-108
On automorphism group of free quadratic extensions over a ring
Mathematics Department, Bradley University, Peoria 61625, Illinois, USA
Received 8 March 1983; Revised 11 November 1983
Copyright © 1984 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 , an automorphism of of order . Then a normal extension of the free quadratic extension with a basis over with an -automorphism group is characterized in terms of the element for in . It is also shown by a different method from the one given by Nagahara that the order of of a Galois extension over with Galois group is a unit in . When is not a zero divisor, more properties of are derived.