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arXiv · 1811.11487

Functors of modules associated with flat and projective modules II

Adrián Gordillo-Merino·José Navarro·Pedro Sancho
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Abstract

Let $R$ be an associative ring with unit. Given an $R$-module $M$, we can associate the following covariant functor from the category of $R$-algebras to the category of abelian groups: $S\mapsto M\otimes_R S$. With the corresponding notion of dual functor, we prove that the natural morphism of functors $\,\mathcal M\to \mathcal M^{\vee\vee}\,$ is an isomorphism. We prove several characterizations of the functors associated with flat modules, flat Mittag-Leffler modules and projective modules.

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Adrián Gordillo-Merino, José Navarro, Pedro Sancho. 2018-11-28. Functors of modules associated with flat and projective modules II. https://arxiv.org/abs/1811.11487

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