Absolutely Clean <i>N</i>-Complexes

The notion of absolutely clean N -complexes is studied. We show that an N -complex [see formula in PDF] is absolutely clean if and only if [see formula in PDF] is N -exact and [see formula in PDF] is an absolutely clean module for each [see formula in PDF] and [see formula in PDF] In particular, we prove that a bounded above N -complex [see formula in PDF] is absolutely clean if and only if [see formula in PDF] is an absolutely clean module for each [see formula in PDF]. We also show that under certain hypotheses, an N -complex [see formula in PDF] is Gorenstein AC-injective if and only if [see formula in PDF] is a Gorenstein AC-injective module for each [see formula in PDF] and [see formula in PDF].