ON CENTRAL COMMUTATOR GALOIS EXTENSIONS OF RINGS

GEORGE SZETO ； LIANYONG XUE

《International Journal of Mathematics and Mathematical Sciences》 2000卷 (2000/12) Pp. a289-294-139

https://doi.org/10.1155/S0161171200004099

摘要

Let B be a ring with 1, G a finite automorphism group of B of order n for some integer n, B^G the set of elements in B fixed under each element in G, and Δ = V_B(B^G) the commutator subring of B^G in B. Then the type of central commutator Galois extensions is studied. This type includes the types of Azumaya Galois extensions and Galois H-separable extensions. Several characterizations of a central commutator Galois extension are given. Moreover, it is shown that when G is inner, B is a central commutator Galois extension of BG if and only if B is an H-separable projective group ring B^GG_f . This generalizes the structure theorem for central Galois algebras with an inner Galois group proved by DeMeyer.

關鍵字

Azumaya algebras ； Galois extensions ； central Galois extensions ； Azumaya Galois extensions ； center Galois extensions ； H-separable extensions