We study the class of standardly stratified algebras
introduced by Cline, Parshall and Scott, and its subclass of
the so-called weakly properly stratified
algebras, which generalizes the class of properly
stratified algebras introduced by Dlab. We characterize when the
Ringel dual of a standardly stratified algebra is weakly properly
stratified and show the existence of a
two-step tilting module. This allows us to calculate
the finitistic dimension of such
algebras. Finally, we also give a construction showing that each
finite partially pre-ordered set gives rise to a weakly properly
stratified algebras with a simple preserving duality.
2004. no 3, p. 38-59