# 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

This article was adapted from an original article by V.E. Govorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article