Cofree Module
A module having dual properties with respect to a free module, as enumerated below.
1. Every free module is projective; every cofree module is injective.
2. For every module 
,
there is a surjective homomorphism from a free module to 
; for every module 
, there is an injective homomorphism from 
to a cofree module.
3. A module is projective iff it can be completed by a direct sum to a free module; a module is injective iff it can be completed by a direct product to a cofree module.
Every cofree module over a unit ring 
is isomorphic to a direct product
indexed on some set 
.
See also
This entry contributed by Margherita Barile
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References
Hilton, P. J. and Stammbach, U. A Course in Homological Algebra, 2nd ed. New York: Springer Verlag, pp. 34-36, 1997.
Referenced on Wolfram|Alpha
Cite this as:
Barile, Margherita. "Cofree Module." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CofreeModule.html