Quasi-hereditary orders
The concept of quasi-hereditary algebra is generalized to rings. This improves a previous definition for quasi-hereditary orders given by the author which comprises classical orders of global dimension two. Moreover, a recent definition of Cline, Parshall, and Scott (1989) which covers integral Schur algebras, is generalized by this new definition of the author. The concept of highest weight category is generalized and yields a class of classical orders which satisfy the new definition of quasi-heredity. It is proved that the category of good lattices over these orders admits almost split sequences.
scientific article; zbMATH DE number 4158873