International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 11, Pages 673-679
doi:10.1155/S0161171203202210
The Boolean algebra of Galois algebras
Department of Mathematics, Bradley University, Peoria 61625, IL, USA
Received 8 February 2002
Copyright © 2003 George Szeto and Lianyong Xue. 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={b∈B|bx=g(x)b for all x∈B} for each g∈G, and
BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero
element in Ba, and He={g∈G|eeg=e}. Then, a
monomial e is characterized, and the Galois extension Be,
generated by e with Galois group He, is investigated.