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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Embedding Galois problems and reduced norms


Author: Teresa Crespo
Journal: Proc. Amer. Math. Soc. 112 (1991), 637-639
MSC: Primary 11E88; Secondary 12F10
MathSciNet review: 1057951
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Abstract: For certain embedding problems $ \tilde G \to G \simeq {\text{Gal}}\left( {L\left\vert K \right.} \right)$ associated to a representation $ t:G \to {\text{Aut}}A$ of the group $ G$ by automorphisms of a central simple $ K$-algebra $ A$ of dimension $ {n^2}$, we prove that the solutions are the fields $ L\left( {{{\left( {rN\left( z \right)} \right)}^{1/n}}} \right)$, with $ r$ running over $ {K^ * }/{K^{ * n}}$ and $ N\left( z \right)$ the reduced norm of an invertible element $ z$ in the algebra $ B \otimes L$, for $ B$ the twisted algebra of $ A$ by $ t$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1057951-1
PII: S 0002-9939(1991)1057951-1
Article copyright: © Copyright 1991 American Mathematical Society