Torsion

Let $𝑀$ be a Module over a ring $𝑅$ . A torsion element $𝑡 \in 𝑅$ is an element that yields zero when multiplied by some non-Zero-divisor $𝜆 \in 𝑅$ , i.e. $𝜆 𝑡 = 0$ . This is a strong deviation from the behaviour of a vector space, as torsion elements cannot exist for a module over a field, where scalar multiplication is injective, hence vector spaces are torsion-free. A torsion module consists of only torsion elements. Given a module, the set of all torsion elements forms the Torsion submodule.

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