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Paper   IPM / M / 16064
School of Mathematics
  Title:   Homotopy category of N-complexes of projective modules
  Author(s): 
1.  Rasool Hafezi
2.  Amin Nematbakhsh (Joint with P. Bahiraei)
  Status:   Published
  Journal: J. Pure Appl. Algebra
  Vol.:  220
  Year:  2016
  Pages:   2414-2433
  Supported by:  IPM
  Abstract:
n this paper, we show that the homotopy category of N-complexes of projective R-modules is triangle equivalent to the homotopy category of projective T_N-1(R)- modules where T_N-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.

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