zero module

Let R be a ring.

The abelian groupMathworldPlanetmath which contains only an identity elementMathworldPlanetmath (zero) gains a trivial R-module structure, which we call the .

Every R-module M has an zero elementMathworldPlanetmath and thus a submoduleMathworldPlanetmath consisting of that element. This is called the zero submodule of M.

Title zero module
Canonical name ZeroModule
Date of creation 2013-03-22 12:01:42
Last modified on 2013-03-22 12:01:42
Owner antizeus (11)
Last modified by antizeus (11)
Numerical id 6
Author antizeus (11)
Entry type Definition
Classification msc 16D10
Synonym zero submodule
Related topic ZeroIdeal