injective module
A module is an injective module 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 a monomorphism and there exists a homomorphism , then there exists a homomorphism such that .
Title | injective module |
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Canonical name | InjectiveModule |
Date of creation | 2013-03-22 12:02:26 |
Last modified on | 2013-03-22 12:02:26 |
Owner | antizeus (11) |
Last modified by | antizeus (11) |
Numerical id | 8 |
Author | antizeus (11) |
Entry type | Definition |
Classification | msc 16D50 |