Homological dimensions of complexes of R-modules

Abstract

Let R be an associative ring with identity, C(R) be the category of com-<br />plexes of R-modules and Flat(C(R)) be the class of all at complexes of R-<br />modules. We show that the at cotorsion theory (Flat(C(R)); Flat(C(R))⁻)<br />have enough injectives in C(R). As an application, we prove that for each at<br />complex F and each complex Y of R-modules, Extⁱ (F,X)= 0, whenever R<br />is n-perfect and i > n.