Free module

In the mathematical field of algebra is a free module is a module which has a base. Thus, the concept of the free module is a generalization of the concepts of vector space or free abelian group.

  • 3.1 Main Features
  • 3.2 Free modules over particular rings

Definition

A family of elements of a module (or more generally of a link module ) is called free, or linearly independent if for every finite index set:

Create the same time the module is the name of a base and the module is called free.

Comments

First examples and counter-examples

The rank of a free module

Many of the theorems about bases of vector spaces are no longer valid at free modules:

Properties of free modules

Main Features

Free modules over particular rings

Attenuations

The following diagram is the freedom of a module over a commutative ring with the properties of projective, flat and torsion- related:

Mathematics Torsion (Algebra) Local ring Projective object
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