Definition:Free Module

Definition

Let $R$ be a ring with unity.

Let $G$ be a unitary $R$-module.

Then $G$ is described as free if and only if there exists a basis of $G$.

Also see

• Bases of Free Module have Equal Cardinality
• Definition:Dimension of Module

• Results about free modules can be found here.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 27$. Subspaces and Bases