投射模的N-复形的同伦范畴
Homotopy category of N-complexes of projective modules
摘要：
本文证明了投射R-模的N-复形的同伦范畴与投射T_{N-1}（R）-模的同伦范畴是三角等价的，其中T_{N-1}（R）是元素在R中的N-1阶三角形矩阵的环。我们还定义了N-奇异范畴和N-完全无圈复形的概念。我们证明了N-生成投射R-模的N-全无圈复形范畴嵌入N-奇异范畴，这一结果类似于普通链复形的情形.
英文摘要：
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 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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