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Embedding orders into central simple algebras

Benjamin Linowitz, Thomas R. Shemanske (2012)

Journal de Théorie des Nombres de Bordeaux

The question of embedding fields into central simple algebras B over a number field K was the realm of class field theory. The subject of embedding orders contained in the ring of integers of maximal subfields L of such an algebra into orders in that algebra is more nuanced. The first such result along those lines is an elegant result of Chevalley [6] which says that with B = M n ( K ) the ratio of the number of isomorphism classes of maximal orders in B into which the ring of integers of L can be embedded...

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