Reflexivity of modules

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 $\mathcal{M}(S):=S{\otimes }_{R}M$ for every $R-$algebra $S$. With the corresponding notion of dual functor, we prove that the natural morphism of functors $\mathcal{M}\to {\mathcal{M}}^{\ast \ast }$ is an isomorphism.

It is re-elaboration of material contained in ArXiv: 1710.04153 (v2)