nLab finitely generated module

Definition

Given a (not necessarily unital) ring $R$, a left $R$-module $(N,\nu)$, is finitely generated if there exists a finite set $S\subseteq N$ such that the canonical morphism from the free module $F(S) \longrightarrow N$ is a surjection.

Related concepts

• generators and relations

• finitely generated object

  • finitely generated algebra

  • finitely generated group

  • finitely presented module

• coherent module

• free module

• Smith normal form

• Eilenberg swindle

References

See also:

• Wikipedia, Finitely generated module