Annihilator

Summary

Let $M$ be a module over a commutative ring $R$. The annihilator of $M$ is the set of elements of $R$ that send every element of $M$ to zero. It is an ideal of $R$. It measures how far the action of $R$ on $M$ is from being faithful. It is used to study the support of a module and the associated primes. It differs from the annihilator of a subspace in linear algebra, which lives in the dual space.