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1991

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/7665

Embedding Galois problems and reduced norms

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https://doi.org/10.2307/2048683
 https://doi.org/10.1090/S0002-9939-1991-1057951-1

Abstract

For certain embedding problems $\tilde{G} \rightarrow G \simeq \operatorname{Gal}(L\mid K)$ associated to a representation $t: G \rightarrow \operatorname{Aut} A$ of the group G by automorphisms of a central simple K-algebra A of dimension n2, we prove that the solutions are the fields L((rN(z))1/n), with r running over K*/K* n and N(z) the reduced norm of an invertible element z in the algebra B ⊗ L, for B the twisted algebra of A by t.

Subject

Teoria algebraica de nombres, Teoria de Galois

Subject (English)

Algebraic number theory, Galois theory

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Citation

CRESPO VICENTE, Teresa. Embedding Galois problems and reduced norms. Proceedings of the American Mathematical Society. 1991. Vol. 112, num. 3, pags. 637-639. ISSN 0002-9939. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/7665

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