associated prime ideal

《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 568 页 · Appendix B.11「Associated Primes」

Let $A$ be a ring and let $M$ be an $A$-module. A prime ideal $\mathfrak p$ of $A$ is called an associated prime ideal of $M$ if there exists an element $m\in M$ such that $\mathfrak p=\operatorname{Ann}(m)=\{a\in A;\ am=0\}$.