associated prime

English

Noun

associated prime (plural associated primes)

1. (algebra, of a module $M$ over a ring $R$) A ideal of $R$ which is the annihilator of some prime submodule of $M$.
   1. (commutative algebra) If the ring $R$ is commutative, equivalently: A prime ideal of $R$ which is the annihilator of some element of $M$.