Tilting modules and exceptional sequences for leaf quotients of type A zig-zag algebras

We classify generalized tilting modules and full exceptional sequences for the family of quasi-hereditary quotients of type A zig-zag algebras and for a related family of algebras. We also give a characterization of these quotients as quasi-hereditary algebras with simple preserving duality that are “close” to self-injective algebras.

k-torsionfree modules with respect to generalized tilting modules

In this paper, the extension closure of the subcategory of mod R consisting of k-torsionfree modules with respect to a generalized tilting bimodule is discussed. Some classical results related to the extension closure of k-torsionfree modules are generalized and strengthened. Let RωS be a cotilting bimodule, the notion of left ⊥ω-approximation dimension is introduced, and as an application, we give a condition such that a ω-k-syzygy module to be ω-k-torsionfree.