# Direct limits of injective modules

Is it true that the direct limit of injective modules is injective?

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See page 81 Theorem 3.46 Lectures on Modules and Rings by Lam. This has exactly the theorem refered to in the comment below and is a nice textbook. –  Conrad Nov 1 '12 at 9:32

Over what ring?

In particular, the answer to your question is "yes" iff the ring is Noetherian.

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To be clearer: the answer is yes for all direct limits of injective module if and only if the ring is noetherian. –  Conrad Nov 1 '12 at 9:35