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
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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