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

George Szeto

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 R be a ring with 1, ρ an automorphism of R of order 2. Then a normal extension of the free quadratic extension R[x,ρ] with a basis {1,x} over R with an R-automorphism group G is characterized in terms of the element (x(x)α) for α in G. It is also shown by a different method from the one given by Nagahara that the order of G of a Galois extension R[x,ρ] over R with Galois group G is a unit in R. When 2 is not a zero divisor, more properties of R[x,ρ] are derived.