  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.
