Homological Behavior of Relative Cotorsionfree and Cosyzygy Modules

Abstract

As the dual of the Auslander transpose and the resulting k-torsionfree module, the cotranspose and k-cotorsionfree module with respect to a semidualizing bimodule have been introduced recently. In this paper we first investigate the relation between relative k-cotorsionfree modules and relative k-cosyzygy modules. Then we study the extension closure of these two classes of modules.