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Glasnik matematički, Vol. 37 No. 1, 2002.

Original scientific paper

Notes on Galois algebras

George Szeto
Lianyong Xue

Full text: english pdf 247 Kb

page 13-19

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Abstract

Let B be a ring with 1, C the center of B, and G an automorphism group of B of order n for some integer n. Assume B is a Galois algebra over R with Galois group G. For a nonzero idempotent e R, it the rank of Be over Ce is defined and equal to the order of H|Be where H = {g G | g(c) = c for each c C}, then Be is a central Galois algebra with Galois group H|Be. This generalizes the F. R. DeMeyer and T. Kanzaki theorems for Galois algebras. Moreover, a structure theorem for a Galois algebra is given in terms of the concept of the rank of projective module.

Keywords

Galois extensions; Galois algebras; central Galois extensions; separable extensions; Azumaya algebras; rank of a projective module

Hrčak ID:

4809

URI

https://hrcak.srce.hr/4809

Publication date:

1.6.2002.

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