Free resolution

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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).


See also Free module.

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