Injective module
From Commalg
This article defines a property of a module over a commutative unital ring
Contents
Definition
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
