Embeddings of fields into simple algebras: generalizations and applications

2011/05/14 by Chia‐Fu Yu, Chia-Fu Yu, Yu, Chia-Fu
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA

paper · pdf · doi:10.48550/arxiv.1105.2895

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

openalex publication_date 2011/05/14 · arxiv created 2012/04/23 · arxiv updated 2012/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^× \backslash \Hom_\falg(A,B) is finite and give an explicit formula for its cardinality. A few applications of main results are given.

Citations

• Embeddings of fields in simple algebras over global fields

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