Injective module

Symbol-free definition
A module over a commutative unital ring is said to be injective if it satisfies the following equivalent conditions:


 * Any short exact sequence of modules with that as the second term, [split short exact sequence of modules|splits]]
 * The covariant functor taking an input module to the module of homomorphisms from this module to the input module, is exact

Related properties

 * Projective module