nLab
finitely generated module

Contents

Context

Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Definition

Given a (not necessarily unital) ring RR, a left RR-module (N,ν)(N,\nu), is finitely generated if there exist a finite set SNS\subset N such that the canonical morphism from the free module F(S)NF(S) \longrightarrow N is a surjection.

References

See also:

Last revised on October 1, 2021 at 11:39:11. See the history of this page for a list of all contributions to it.