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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 3

Homological dimensions of complexes related to cotorsion pairs

Chongqing WEI
Limin WANG
Husheng QIAO
Pages
401–418
Publication Date
2014-05-16
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, we characterize Noetherian rings, von Neumann regular rings, and QF rings by the FP-projective, FP-injective, and Ding projective (injective) dimension of complexes, respectively.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let (A, B) be a cotorsion pair in R-Mod.
📊
Key Findings & Data:We define and study notions of A dimension and B dimension of unbounded complexes, which is given by means of dg-projective resolution and dg-injective resolution, respectively.
💡
Conclusion & Impact:Moreover, we characterize Noetherian rings, von Neumann regular rings, and QF rings by the FP-projective, FP-injective, and Ding projective (injective) dimension of complexes, respectively.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cotorsion pairs · A dimension of complexes · B dimension of complexes

Abstract

Let (A, B) be a cotorsion pair in R-Mod. We define and study notions of A dimension and B dimension of unbounded complexes, which is given by means of dg-projective resolution and dg-injective resolution, respectively. As an application, we extend the Gorenstein flat dimension of complexes, which was defined by Iacob. Gorenstein cotorsion, FP-projective, FP-injective, Ding projective, and Ding injective dimension are also extended from modules to complexes. Moreover, we characterize Noetherian rings, von Neumann regular rings, and QF rings by the FP-projective, FP-injective, and Ding projective (injective) dimension of complexes, respectively.

Özet

Let (A, B) be a cotorsion pair in R-Mod. We define and study notions of A dimension and B dimension of unbounded complexes, which is given by means of dg-projective resolution and dg-injective resolution, respectively. As an application, we extend the Gorenstein flat dimension of complexes, which was defined by Iacob. Gorenstein cotorsion, FP-projective, FP-injective, Ding projective, and Ding injective dimension are also extended from modules to complexes. Moreover, we characterize Noetherian rings, von Neumann regular rings, and QF rings by the FP-projective, FP-injective, and Ding projective (injective) dimension of complexes, respectively.

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Cite This Article

WEI, C., WANG, L., QIAO, H. (2014). Homological dimensions of complexes related to cotorsion pairs. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 3, 401–418. https://ajindex.com/articles/185726

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