On the existence of maximal orders

Details On the existence of maximal orders On the existence of maximal orders

2011-05-14

arxiv.org/abs/1105.2897v1

Mathematics

Number Theory

22 pages. To appear in Int. J. Number Theory

Scientific paper

We generalize the existence of maximal orders in a semi-simple algebra for general ground rings. We also improve several statements in Chapter 5 and 6 of Reiner's book concerning separable algebras by removing the separability condition, provided the ground ring is only assumed to be Japanese, a very mild condition. Finally, we show the existence of maximal orders as endomorphism rings of abelian varieties in each isogeny class.

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