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 ${\displaystyle M}$ .