What is the meaning of Associated_prime?

A ideal of ${\displaystyle R}$ which is the annihilator of some prime submodule of ${\displaystyle M}$.

1. If the ring ${\displaystyle R}$ is commutative, equivalently: A prime ideal of ${\displaystyle R}$ which is the annihilator of some element of ${\displaystyle M}$.

If the ring ${\displaystyle R}$ is commutative, equivalently: A prime ideal of ${\displaystyle R}$ which is the annihilator of some element of ${\displaystyle M}$.

Source: wiktionary.org