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Baer's Criterion


Baer's criterion, also known as Baer's test, states that a module M over a unit ring R is injective iff every module homomorphism from an ideal of R to M can be extended to a homomorphism from R to M.


See also

Commutative Diagram, Injective Module

This entry contributed by Margherita Barile

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References

Baer, R. "Abelian Groups that Are Direct Summands of Every Containing Abelian Group." Bull. Amer. Math. Soc. 46, 800-806, 1940.Faith, C. Algebra: Rings, Modules and Categories, I. Berlin, p. 157, 1973.Lam, T. Y. Lectures on Modules and Rings. New York: Springer-Verlag, p. 63, 1999.

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Baer's Criterion

Cite this as:

Barile, Margherita. "Baer's Criterion." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/BaersCriterion.html

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