Torsion modules

Torsion modules are mathematical structures that study how elements within a module can be "annihilated" or vanish when multiplied by certain non-zero elements of a ring. Think of a torsion element as one that turns into zero when scaled by some non-zero factor. Torsion modules consist entirely of such elements and help mathematicians understand the behavior of modules over rings, especially in algebraic contexts like number theory and algebraic geometry. They reveal the parts of a module that are "finite" or "degenerate" under multiplication, providing insight into its structure and properties.