Optimal embeddings in quaternion algebras

C. MacLachlan

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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 Rk denote the ring of integers of k and let B be an Rk-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 s : L¿A over k which gives an optimal embedding of B into E in the sense that s(L)nE = s(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].
Original languageEnglish
Pages (from-to)2852-2860
Number of pages9
JournalJournal of Number Theory
Issue number10
Publication statusPublished - Oct 2008


  • quaternion algebra
  • order
  • maximal order
  • Eichler order


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