Torsion (algebra)

In algebra, particularly in the context of module theory, torsion refers to a property of elements in a module over a ring. More specifically, let \( M \) be a module over a ring \( R \). An element \( m \in M \) is said to be a torsion element if there exists a non-zero element \( r \in R \) such that \( r \cdot m = 0 \).