Finiteness conditions and cotorsion pairs

DOI10.1016/J.JPAA.2016.09.008zbMATH Open1362.18019arXiv1510.08966OpenAlexW2240732280MaRDI QIDQ503793

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Publication date: 23 January 2017

Published in: (Search for Journal in Brave)

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 ${mExt}_R^1(F,-)$ and ${mTor}_1^R(F,-)$. We also construct cotorsion pairs from these orthogonal complements, allowing us to provide further characterizations of $n$-coherent rings.

Full work available at URL: https://arxiv.org/abs/1510.08966

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