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- W2013716011 abstract "Let A be a quaternion algebra over a number field k and assume that A satisfies the Eichler condition so that some infinite place of k is unramified in A . Let L be a quadratic extension of k which embeds in A . Let R k denote the ring of integers of k and let B be an R k -order in L . Suppose that E is an Eichler order of A of square-free level S . In this paper, we determine when there exists an embedding σ : L → A over k which gives an optimal embedding of B into E in the sense that σ ( L ) ∩ E = σ ( B ) . This generalises previous work of Eichler [M. Eichler, Zur Zahlentheorie der Quaternionenalgebren, J. Reine Angew. Math. 195 (1955) 127–155] and Chinburg and Friedman [T. Chinburg, E. Friedman, An embedding theorem for quaternion algebras, J. London Math. Soc. 60 (1999) 33–44]." @default.
- W2013716011 created "2016-06-24" @default.
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- W2013716011 date "2008-10-01" @default.
- W2013716011 modified "2023-10-16" @default.
- W2013716011 title "Optimal embeddings in quaternion algebras" @default.
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- W2013716011 doi "https://doi.org/10.1016/j.jnt.2007.12.007" @default.
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