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On central commutator Galois extensions of rings

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  • George Szeto
  • Lianyong Xue

Abstract

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 B G if and only if B is an H -separable projective group ring B G G f . This generalizes the structure theorem for central Galois algebras with an inner Galois group proved by DeMeyer.

Suggested Citation

  • George Szeto & Lianyong Xue, 2000. "On central commutator Galois extensions of rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:284510
    DOI: 10.1155/S0161171200004099
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