k-torsionfree modules with respect to generalized tilting modules

Abstract

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.