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arXiv · 1105.2895

Embeddings of fields into simple algebras: generalizations and applications

Chia-Fu Yu
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Abstract

For two semi-simple algebras $A$ and $B$ over an arbitrary ground field $F$, we give a numerical criterion when $\Hom_F(A,B)$, the set of $F$-algebra homomorphisms between them, is non-empty. We also determine when the orbit set $B^\times \backslash \Hom_\falg(A,B)$ is finite and give an explicit formula for its cardinality. A few applications of main results are given.

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Chia-Fu Yu. 2011-05-14. Embeddings of fields into simple algebras: generalizations and applications. https://arxiv.org/abs/1105.2895

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