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International Journal of Mathematics and Mathematical Sciences - Volume 3 1980, Issue 2, Pages 237-245

Department of Mathematics, Bradley University, Peoria 61625, Illinois, USA

Received 1 February 1979; Revised 13 July 1979

Copyright © 1980 Hindawi Publishing Corporation. 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.

Abstract

Let B be a commutative ring with 1, and G={σ} an automorphism group of B of order 2. The generalized quaternion ring extension Bj over B is defined by S. Parimala and R. Sridharan such that 1 Bj is a free B-module with a basis {1,j}, and 2 j2=−1 and jb=σbj for each b in B. The purpose of this paper is to study the separability of Bj. The separable extension of Bj over B is characterized in terms of the trace =1+σ of B over the subring of fixed elements under σ. Also, the characterization of a Galois extension of a commutative ring given by Parimala and Sridharan is improved.





Autor: George Szeto

Fuente: https://www.hindawi.com/



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