On the existence of maximal orders
  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. 
Chia-Fu Yu
math.NT