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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 11, Pages 673-679
http://dx.doi.org/10.1155/S0161171203202210

The Boolean algebra of Galois algebras

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

Received 8 February 2002

Copyright © 2003 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 Galois algebra with Galois group G, Jg={bB|bx=g(x)bfor allxB} for each gG, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|gG}, e a nonzero element in Ba, and He={gG|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generated by e with Galois group He, is investigated.