International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 4, Pages 237-242
doi:10.1155/S0161171201007104
The Boolean algebra and central Galois algebras
Department of Mathematics, Bradley University, Peoria 61625, IL, USA
Received 15 March 2001
Copyright © 2001 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 g∈G, and BJg=Beg for a central idempotent eg. Then a relation is given between the set of elements in the Boolean algebra (Ba,≤) generated by {0,eg∣g∈G} and a set of subgroups of G, and a central Galois algebra Be with a Galois subgroup of G is characterized for an e∈Ba.