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arXiv · 1510.08966

Finiteness conditions and cotorsion pairs

Daniel Bravo·Marco A. Pérez
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Abstract

We study the interplay between the notions of $n$-coherent rings and finitely $n$-presented modules, and also study the relative homological algebra associated to them. We show that the $n$-coherency of a ring is equivalent to the thickness of the class of finitely $n$-presented modules. The relative homological algebra part comes from the study of orthogonal complements to this class of modules with respect to ${\rm Ext}^1_R(F,-)$ and ${\rm Tor}_1^R(F,-)$. We also construct cotorsion pairs from these orthogonal complements, allowing us to provide further characterizations of $n$-coherent rings.

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BibTeXRIS

Daniel Bravo, Marco A. Pérez. 2015-10-30. Finiteness conditions and cotorsion pairs. https://doi.org/10.1016/j.jpaa.2016.09.008

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