The Galois extensions induced by idempotents in a Galois algebra
Let be a Galois algebra with Galois group , for each , the central idempotent such that , and for a subgroup of . Then is a Galois extension with the Galois group containing and the normalizer of in . An equivalence condition is also given for , and is shown to be a direct sum of all generated by a minimal idempotent . Moreover, a characterization for a Galois extension is shown in terms of the Galois extension and .