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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 M, there is a surjective homomorphism from a free module to M; for every module M, there is an injective homomorphism from M 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 R is isomorphic to a direct product

 product_(I)Hom_Z(R,Q/Z)

indexed on some set I.


See also

Free Module

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

Cofree Module

Cite this as:

Barile, Margherita. "Cofree Module." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CofreeModule.html

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