✦ LIBER ✦

The Structure of Galois Algebras

✍ Scribed by George Szeto; Lianyong Xue

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 87 KB
Volume: 237
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8568

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✦ Synopsis

Let B be a ring with 1 and G an automorphism group of B of order n for some integer n. It is shown that if B is a Galois algebra with Galois group G, then B is either a direct sum of central Galois algebras or a direct sum of central Galois algebras and a commutative Galois algebra. Moreover, when G is inner, B is either a direct sum of Azumaya projective group algebras or a direct sum of Azumaya projective group algebras and a commutative Galois algebra. Examples are given for these structures.

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