Galois extensions induced by a central idempotent in a partial Galois extension

Abstract

Let (R,α) be a partial Galois extension of RαG with a partial action of a finite group G, e a non-zero central idempotent in R, 1g the central idempotent associated with g ∈ G, and E = e(Πg∈G1g) 6= 0 with a maximal number of factors 1g for g ∈ G. A sufficient condition for a Galois extension Re with Galois group H(e) and for a Galois extension RE with Galois group N(e) is given respectively, where H(e) = {g ∈ G|e1g = e} and N(e) = {g ∈ G|e(Πg∈G1g) 6= 0} with a maximal number of factors 1g for g ∈ G. This leads to a structure of Re as a direct sum of Galois extensions. Mathematics Subject Classification: 13B05