Free resolution
From Encyclopedia of Mathematics
A special case of a projective resolution. Every module 
over an associative ring 
is the quotient module 
of a free 
-module 
by a submodule 
. The submodule 
has a similar representation 
, etc. As a result one obtains an exact sequence of free modules
 |
called the free resolution of 
. The canonical homomorphism 
is called a supplementing homomorphism (or augmentation).
Comments
See also Free module.
How to Cite This Entry:
Free resolution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Free_resolution&oldid=12844
Free resolution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Free_resolution&oldid=12844
This article was adapted from an original article by V.E. Govorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article