Open Access
April 2014 Embeddings of fields into simple algebras over global fields
Sheng-Chi Shih, Tse-Chung Yang, Chia-Fu Yu
Asian J. Math. 18(2): 365-386 (April 2014).


Let $F$ be a global field, $A$ a central simple algebra over $F$, and $K$ a finite (separable or not) field extension of $F$ with degree $[K : F]$ dividing the degree of $A$ over $F$. An embedding of $K$ into $A$ over $F$ exists implies an embedding exists locally everywhere. In this paper we give detailed discussions about when the converse (i.e. the local-global principle in question) may hold.


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Sheng-Chi Shih. Tse-Chung Yang. Chia-Fu Yu. "Embeddings of fields into simple algebras over global fields." Asian J. Math. 18 (2) 365 - 386, April 2014.


Published: April 2014
First available in Project Euclid: 27 August 2014

zbMATH: 1316.11107
MathSciNet: MR3217641

Primary: 11E72 , 17C20

Keywords: Central simple algebras , embeddings , Galois cohomology , the Hasse principle

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 2 • April 2014
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