Definition 15.117.1. Let $R$ be a ring. An $R$-module $M$ is *invertible* if the functor

\[ \text{Mod}_ R \longrightarrow \text{Mod}_ R,\quad N \longmapsto M \otimes _ R N \]

is an equivalence of categories. An invertible $R$-module is said to be *trivial* if it is isomorphic to $R$ as an $R$-module.

## Comments (2)

Comment #6341 by Yuto Masamura on

Comment #6442 by Johan on