Homotopy category of N-complexes of projective modules

In this paper, we show that the homotopy category of N-complexes of projective R-modules is triangle equivalent to the homotopy category of projective TN−1(R)-modules where TN−1(R) is the ring of triangular matrices of order N−1 with entries in R. We also define the notions of N-singularity category...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2016-06, Vol.220 (6), p.2414-2433
Main Authors: Bahiraei, P., Hafezi, R., Nematbakhsh, A.
Format: Article
Language:English
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Summary:In this paper, we show that the homotopy category of N-complexes of projective R-modules is triangle equivalent to the homotopy category of projective TN−1(R)-modules where TN−1(R) is the ring of triangular matrices of order N−1 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 embeds in the N-singularity category, which is a result analogous to the case of ordinary chain complexes.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2015.11.012