projective cover

Let X and P be modules. We say that P is a projective cover of X if P is a projective moduleMathworldPlanetmath and there exists an epimorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath p:PX such that kerp is a superfluous submodule of P.

Equivalently, P is an projective cover of X if P is projective, and there is an epimorphism p:PX, and if g:PX is an epimorphism from a projective module P to X, then there exists an epimorphism h:PP such that ph=g.

Title projective cover
Canonical name ProjectiveCover
Date of creation 2013-03-22 12:10:08
Last modified on 2013-03-22 12:10:08
Owner antizeus (11)
Last modified by antizeus (11)
Numerical id 6
Author antizeus (11)
Entry type Definition
Classification msc 16D40