associated prime

Let R be a ring, and let M be an R-module. A prime idealMathworldPlanetmathPlanetmathPlanetmath P of R is an for M if P=ann(X), the annihilatorPlanetmathPlanetmathPlanetmathPlanetmath of some nonzero submodule X of M.

Note that if this is the case, then the module annM(P) contains X, has P as its annihilator, and is a faithful ( (R/P)-module.

If, in addition, P is equal to the annihilator of a submodule of M that is a fully faithful ( (R/P)-module, then we call P an of M.

Title associated prime
Canonical name AssociatedPrime
Date of creation 2013-03-22 12:01:37
Last modified on 2013-03-22 12:01:37
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 10
Author rspuzio (6075)
Entry type Definition
Classification msc 16D25
Synonym annihilator prime