The Boolean algebra and central Galois algebras

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.