Asian Journal of Mathematics

Volume 18 (2014)

Number 2

Embeddings of fields into simple algebras over global fields

Pages: 365 – 386



Sheng-Chi Shih (Institute of Mathematics, Academia Sinica, Taipei, Taiwan)

Tse-Chung Yang (Department of Mathematics, National Taiwan University, Taipei, Taiwan)

Chia-Fu Yu (Institute of Mathematics, Academia Sinica, Taipei, Taiwan)


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.


central simple algebras, embeddings, the Hasse principle, Galois cohomology

2010 Mathematics Subject Classification

11E72, 17C20

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