Projective 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 projective if it satisfies the following equivalent conditions:
- Any short exact sequence of modules with that as the fourth term, splits
- It is a direct summand of a free module
- The contravariant functor sending a module to the module of homomorphisms from that module, to this one, is exact
