associated prime

associated prime (plural associated primes)

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