I was wondering if someone could be so kind as to provide an example of a local ring $ (R,\frak{m}) $ and a non-free finitely generated injective module over $ R $. Thank you very much! I tried searching everywhere online, but my attempts have been a total failure so far.
Non-Free Finitely Generated Injective Modules over a Local Ring
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commutative-algebra
ring-theory
modules
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0@HaskellCurry you're welcome. I don't know if it's in Lam's book I'm afraid. – 2012-12-10
1 Answers
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An example would be $R = k[x,y]/(xy,x^2,y^2), \mathfrak{m}=(x,y)$, with $I$ the unique indecomposable injective.