Quasi-hereditary orders

Quasi-hereditary rings are defined as generalizations of quasi-hereditary algebras; it is shown that some of the main properties of quasi-hereditary algebras carry over to quasi-hereditary rings. In particular, a generalization of the concept of highest weight categories gives a class of classical orders which satisfy our definition of quasi-heredity. For this class of orders the category of good lattices is investigated and it is shown that this category has almost split sequences.