In
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
* Mo ...
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 d ...
.
* 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 ele ...
*
Eilenberg–Mazur swindle
*
Hermite ring In algebra, the term Hermite ring (after Charles Hermite) has been applied to three different objects.
According to (p. 465), a ring is right Hermite if, for every two elements ''a'' and ''b'' of the ring, there is an element ''d'' of the ring an ...
References
{{Reflist
Module theory
Free algebraic structures