Injective module

This article defines a property of a module over a commutative unital ring

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

Relation with other properties

Related properties

• Projective module