projective module
A module is projective if it satisfies the following equivalent conditions:
(a) Every short exact sequence of the form is split (http://planetmath.org/SplitShortExactSequence);
(b) The functor is exact (http://planetmath.org/ExactFunctor);
(c) If is an epimorphism and there exists a homomorphism , then there exists a homomorphism such that .
(d) The module is a direct summand of a free module.
Title | projective module |
---|---|
Canonical name | ProjectiveModule |
Date of creation | 2013-03-22 12:09:42 |
Last modified on | 2013-03-22 12:09:42 |
Owner | antizeus (11) |
Last modified by | antizeus (11) |
Numerical id | 7 |
Author | antizeus (11) |
Entry type | Definition |
Classification | msc 16D40 |
Related topic | InvertibleIdealsAreProjective |