Corpus ID: 226979798

An explicit self-dual construction of complete cotorsion pairs in the relative context

@article{Positselski2020AnES,
title={An explicit self-dual construction of complete cotorsion pairs in the relative context},
author={L. Positselski},
journal={arXiv: Rings and Algebras},
year={2020}
}
Let $R\to A$ be a homomorphism of associative rings, and let $(\mathcal F,\mathcal C)$ be a hereditary complete cotorsion pair in $R\mathsf{-Mod}$. Let $(\mathcal F_A,\mathcal C_A)$ be the cotorsion pair in $A\mathsf{-Mod}$ in which $\mathcal F_A$ is the class of all left $A$-modules whose underlying $R$-modules belong to $\mathcal F$. Assuming that the $\mathcal F$-resolution dimension of every left $R$-module is finite and the class $\mathcal F$ is preserved by the coinduction functor… Expand

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