Associated prime to a module

From Commalg
Jump to: navigation, search


Let R be a commutative unital ring and M be a R-module. A prime ideal P of R is said to be associated to M if it satisfies the following equivalent conditions:

  • P is the annihilator of an element of M
  • There is an injective homomorphism A/P \to M of A-modules

The set of all primes associated to M is denoted as Ass_RM.