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Finiteness conditions and cotorsion pairs. (English) Zbl 1362.18019
The authors consider the classes of finitely \(n\)-presented modules \(\mathcal{FP}_n\) and \(n\)-coherent rings and establish a characterization of \(n\)-coherent rings in terms of finitely \(n\)-presented modules.
Then, the relative homological algebra with respect to the class \(\mathcal{FP}_n\), from the injective and flat properties is studied to get the classes of modules \(\mathcal{FP}_n\)-Inj and \(\mathcal{FP}_n\)-Flat, respectively. Some of the presented results on this matter are adopted from D. Bravo, J. Gillespie and M. Hovey [“The stable module category of a general ring”, Preprint, arXiv:1405.5768] and J. Chen and N. Ding [Commun. Algebra 24, No. 10, 3211–3216 (1996; Zbl 0877.16010)].
At the end, the completeness of certain cotorsion pairs associated to the classes \(\mathcal{FP}_n\)-Inj and \(\mathcal{FP}_n\)-Flat is investigated.

MSC:
18G25 Relative homological algebra, projective classes (category-theoretic aspects)
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
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