Is it true that the direct limit of injective modules is injective?
Direct limits of injective modules
2
$\begingroup$
commutative-algebra
ring-theory
modules
-
0See 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. – 2012-11-01
1 Answers
1
Over what ring?
In particular, the answer to your question is "yes" iff the ring is Noetherian.
-
0To be clearer: the answer is yes for all direct limits of injective module if and only if the ring is noetherian. – 2012-11-01