Let G be a group, F a field, and A a finite-dimensional central simple algebra over F on which G acts by F-algebra automorphisms. We study the subalgebras and ideals of A which are preserved by the group action. We prove a structure theorem and two classification theorems for invariant subalgebras u
On central simple algebras of given exponent
β Scribed by Darrell E Haile
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 867 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0021-8693
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π SIMILAR VOLUMES
Let A be a finite-dimensional central simple algebra and let k be a subfield of Ε½ . its center Z A . We say that z , . . . , z generate A as a central simple algebra we give a necessary and sufficient condition for A to be generated by m elements as a central simple algebra over k.
A splitting field of a central simple algebra is said to be absolute Galois if it is Galois over some fixed subfield of the centre of the algebra. The paper proves an existence theorem for such fields over global fields with enough roots of unity. As an application, all twisted function fields and a