Free module

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

Definition

A module over a commutative unital ring is said to be free if it has a free generating set, viz a generating set such that every element of the ring can be written uniquely as a combination of elements of the generating set with coefficients in the ring.

Relation with other properties

Weaker properties

• Stably free module
• Projective module
• Flat module