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Show that the set of the R-homomorphism $A\rightarrow B$ with factorization through an injective module is an subgroup of $Hom_{R}(A,B)$.

It's a question from my last test in abstract algebra, that I can't solve.

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If $f:A\to B$ factors through the injective $I$, and $g:A\to B$ factors through the injective $J$, what injective does $f+g$ factor through? Remember that the direct product of two injective modules is injective... – Mariano Suárez-Alvarez Nov 21 '10 at 4:28
Gracias Mariano, gran ayuda – Bryan Yocks Nov 21 '10 at 15:33
up vote 2 down vote accepted

Hint: This just follows from the fact that a direct sum of two injective modules is injective.

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Thanks Timothy .. – Bryan Yocks Nov 21 '10 at 15:34

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