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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 11, Pages 753-758
http://dx.doi.org/10.1155/S0161171200003562

On characterizations of a center Galois extension

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

Received 16 June 1999

Copyright © 2000 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 ring with 1,C the center of B,G a finite automorphism group of B, and BG the set of elements in B fixed under each element in G. Then, it is shown that B is a center Galois extension of BG (that is, C is a Galois algebra over CG with Galois group G|CG) if and only if the ideal of B generated by {cg(c)|cC} is B for each g1 in G. This generalizes the well known characterization of a commutative Galois extension C that C is a Galois extension of CG with Galois group G if and only if the ideal generated by {cg(c)|cC} is C for each g1 in G. Some more characterizations of a center Galois extension B are also given.