The Stacks project

Definition 15.22.1. Let $R$ be a domain. Let $M$ be an $R$-module.

  1. We say an element $x \in M$ is torsion if there exists a nonzero $f \in R$ such that $fx = 0$.

  2. We say $M$ is torsion free if the only torsion element of $M$ is $0$.

  3. We say $M$ is a torsion module if every element of $M$ is torsion.

Comments (2)

Comment #9795 by Laurent Moret-Bailly on

According to section 15.89, this should include a definition of torsion modules.

There are also:

  • 2 comment(s) on Section 15.22: Torsion free modules

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View Definition 15.22.1 as pdf