Embeddings of fields into simple algebras: generalizations and applications

Details Embeddings of fields into simple algebras: generalizations and applications Embeddings of fields into simple algebras: generalizations and applications

2011-05-14

arxiv.org/abs/1105.2895v3

Mathematics

Rings and Algebras

19 pages; Section 4 of v2 is removed and moves to arXiv:1108.0830. Add new Section 4 for more applications

Scientific paper

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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