  Let R be a two-sided noetherian ring. Auslander and Bridger developed a
theory of projective stabilization of the category of finitely generated
R-modules, which is called the stable module theory. Recently, Yoshino
established a stable ''complex'' theory, i.e., a theory of a certain
stabilization of the homotopy category of complexes of finitely generated
projective R-modules. We introduce higher versions of several notions
introduced by Yoshino, such as *torsionfreeness and *reflexivity. Also, we
prove the Auslander-Bridger approximation theorem for complexes of finitely
generated projective R-modules.

Commutative Algebra;Rings and Algebras;Representation Theory