faithful module

Let R be a ring, and let M be an R-module. We say that M is a faithful R-module if its annihilatorPlanetmathPlanetmathPlanetmathPlanetmath annR(M) is the zero idealMathworldPlanetmathPlanetmath.

We say that M is a fully faithful R-module if every nonzero R-submodule of M is faithful.

Title faithful module
Canonical name FaithfulModule
Date of creation 2013-03-22 12:01:35
Last modified on 2013-03-22 12:01:35
Owner antizeus (11)
Last modified by antizeus (11)
Numerical id 7
Author antizeus (11)
Entry type Definition
Classification msc 16D80
Synonym fully faithful module