Torsion module

A torsion module over an integral domain is a module in which every element is annihilated by some nonzero scalar.

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- Torsion submodule Torsion module

Torsion submodule ( $T (M)$ )

For a module

M

over an integral domain

R

, its torsion submodule is

T (M) = {m \in M : r m = 0 for some 0 \neq = r \in R} .

The domain condition makes this a submodule: products of nonzero annihilators remain nonzero and annihilate sums.

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Past exam of the mathematics course of the University of Cambridge / 2020 / ib / Paper 1 / 9G / Solution

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