k-torsionfree modules with respect to generalized tilting modules

摘要

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 R omega S be a cotilting bimodule, the notion of left (perpendicular to)omega-approximation dimension is introduced, and as an application, we give a condition such that a omega-ksyzygy module to be omega-k-torsionfree.