Reflexivity of modules

2018/06/26 by Adrián Gordillo-Merino, José Navarro, Gordillo-Merino, Adrián +3
Mathematics · #16D10 #18A99 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1806.09892

openalex publication_date 2018/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider R-modules as functors in the following way: if M is a (left) R-module, let \mathcal M be the functor of \mathcal R-modules defined by \mathcal M(S) := S ⊗_R M for every R-algebra S. With the corresponding notion of dual functor, we prove that the natural morphism of functors \mathcal M→ \mathcal M^** is an isomorphism.

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