Cartan–Eilenberg complexes with respect to cotorsion pairs

Lu, Bo; Liu, Zhong Kui

doi:10.1007/s00013-013-0605-1

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…Therefore, Cartan-Eilenberg complexes play an important role in the category of complexes and the homotopy category. In [9,13,14,26], the authors also considered Cartan-Eilenberg complexes and obtained some important results. For instance, Enochs proved that every complex has a Cartan-Eilenberg injective envelope, every complex has a Cartan-Eilenberg projective precover and a complex is Cartan-Eilenberg flat if and only if it is the direct limit of finitely generated Cartan-Eilenberg projective complexes [9].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, Enochs proved that every complex has a Cartan-Eilenberg injective envelope, every complex has a Cartan-Eilenberg projective precover and a complex is Cartan-Eilenberg flat if and only if it is the direct limit of finitely generated Cartan-Eilenberg projective complexes [9]. In [13,14,26], the authors investigated the Cartan-Eilenberg Gorenstein complexes, the stability of Cartan-Eilenberg Gorenstein categories and established some relationships between Cartan-Eilenberg complexes and DG complexes.…”

Section: Introductionmentioning

confidence: 99%

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Cartan–eilenberg Fp-Injective Complexes

Lu¹,

Liu²

2016

J. Aust. Math. Soc.

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In this article, we extend the notion of FP-injective modules to that of Cartan–Eilenberg complexes. We show that a complex $C$ is Cartan–Eilenberg FP-injective if and only if $C$ and $\text{Z}(C)$ are complexes consisting of FP-injective modules over right coherent rings. As an application, coherent rings are characterized in various ways, using Cartan–Eilenberg FP-injective and Cartan–Eilenberg flat complexes.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cartan–eilenberg Fp-Injective Complexes

Lu¹,

Liu²

2016

J. Aust. Math. Soc.

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“…Therefore, Cartan-Eilenberg complexes play an important role in the category of complexes and the homotopy category. In [6] and [20], the authors also considered Cartan-Eilenberg complexes. In the present article, we will study Gorenstein projective complexes using Cartan-Eilenberg complexes.…”

Section: Introductionmentioning

confidence: 99%

A note on Gorenstein projective complexes

Lu¹,

Liu²

2016

Turk J Math

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As we know, a complex Q is projective if and only if Q is exact and Zn(Q) is projective in R-Mod for each n ∈ Z. In this article, we show that a complex G is Gorenstein projective with Hom R(P, G) and Hom R(G, P) exact for any Cartan-Eilenberg projective complex P if and only if G is exact and Zn(G) is Gorenstein projective in R-Mod for each n ∈ Z. Using the above result, a new equivalent characterization of some A complexes is obtained.

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Cartan-Eilenberg N-complexes with respect to self-orthogonal subcategories

Liu

2020

Front. Math. China

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Cartan–Eilenberg complexes with respect to cotorsion pairs

Cited by 3 publications

References 13 publications

Cartan–eilenberg Fp-Injective Complexes

Cartan–eilenberg Fp-Injective Complexes

A note on Gorenstein projective complexes

Cartan-Eilenberg N-complexes with respect to self-orthogonal subcategories

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