Homotopy category of N-complexes of projective modules

Payam Bahiraei, Rasool Hafezi, Amin Nematbakhsh

Published 2015-04-04Version 1

In this paper, we show that the homotopy category of N-complexes of pro- jective R-modules is triangle equivalent to the homotopy category of projective T_N(R)- module where T_N(R) is the ring of triangular matrix with entries in R. We also define the notions of N-singularity category and N-totally acyclic complexes. We show that the category of N-totally acyclic complexes of finitely generated projective R-modules em- beds in the N-singularity category, i.e. a result analogous to the case of ordinary chain complexes.