$\Delta$-Filtrations and Projective Resolutions for the Auslander-Dlab-Ringel Algebra


The ADR algebra $R_A$ of an Artin algebra $A$ is a right ultra strongly quasihereditary algebra (RUSQ algebra). In this paper we study the $\Delta$-filtrations of modules over RUSQ algebras and determine the projective covers of a certain class of $R_A$-modules. As an application, we give a counterexample to a claim by Auslander-Platzeck-Todorov, concerning projective resolutions over the ADR algebra.

Algebras and Representation Theory, 21, no. 3, pp. 605-625