Cartan-Eilenberg N-complexes with respect to self-orthogonal subcategories
Cartan-Eilenberg N-complexes with respect to self-orthogonal subcategories
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DOI：
10.1007/s11464-020-0828-y
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发表时间：
2020-04
影响因子：
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通讯作者：
Bo Lu;Zhenxing Di;Yifu Liu
中科院分区：
文献类型：
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作者：
Bo Lu;Zhenxing Di;Yifu Liu
设R是任意的相联环。对于整数N ≠ 2和R-模的自正交子范畴，我们研究了Cartan-EilenbergN-复形的概念.证明了N-复形X是Cartan-Eilenbergi f且仅当X <$X′ <$X″，其中X ′是N-复形且X ″是分次R-模，且X ″n∈，对所有n ∈ <$。作为结果的应用，我们得到了Cartan-Eilenberg投射和内射N-复形的一些特征，建立了N-复形的Cartan和Eilenberg平衡，并给出了一些固定整数N的例子来说明我们的主要结果。
LetRbe an arbitrary associated ring. For an integerN⩾ 2 and a self-orthogonal subcategoryofR-modules, we study the notion of Cartan-EilenbergN-complexes. We show that anN-complexXis Cartan-Eilenbergif and only ifX≅X′ ⊕X″ in whichX′ is aN-complex andX″ is a gradedR-module withX″n∈for alln∈ ℤ. As applications of the result, we obtain some characterizations of Cartan-Eilenberg projective and injectiveN-complexes, establish Cartan and Eilenberg balance ofN-complexes, and give some examples for some fixed integersNto illustrate our main results.