Associated prime

Summary

An associated prime of a module $M$ over a commutative ring is a prime ideal that is the annihilator of a single element of $M$. For a finitely generated module over a Noetherian ring, there are only finitely many, and their union is the set of zero divisors on $M$. When $R$ is Noetherian, the associated primes of $R/I$ are the primes that appear in a primary decomposition of the ideal $I$.