In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a stably free module is a
module
Module, modular and modularity may refer to the concept of modularity. They may also refer to:
Computing and engineering
* Modular design, the engineering discipline of designing complex devices using separately designed sub-components
* Modul ...
which is close to being
free.
Definition
A finitely generated module ''M'' over a ring ''R'' is ''stably free'' if there exist free finitely generated modules ''F'' and ''G'' over ''R'' such that
:
Properties
* A projective module is stably free if and only if it possesses a finite
free resolution In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution) is an exact sequence of modules (or, more generally, of objects of an abelian category), which is used to defi ...
.
* An
infinitely generated module is stably free if and only if it is free.
See also
*
Free object
In mathematics, the idea of a free object is one of the basic concepts of abstract algebra. Informally, a free object over a set ''A'' can be thought of as being a "generic" algebraic structure over ''A'': the only equations that hold between eleme ...
*
Eilenberg–Mazur swindle
In mathematics, the Eilenberg–Mazur swindle, named after Samuel Eilenberg and Barry Mazur, is a method of proof that involves paradoxical properties of infinite sums. In geometric topology it was introduced by and is often called the Mazur swi ...
*
Hermite ring In Abstract_algebra, algebra, the term Hermite ring (after Charles Hermite) has been applied to three different objects.
According to (p. 465), a ring (mathematics), ring is right Hermite if, for every two elements ''a'' and ''b'' of the ring, the ...
References
{{Reflist
Module theory
Free algebraic structures