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YCor
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injective modules and divisible modules

The following result is basic ( P.J.Hilton, U.Stammabach, a course in homological algebra ).

Let $A$ be a principal ideal domain. Then a $A$ module is injective iff it is divisible.

Now if the condition is "Let $A$ be a domain", does the result hold ? I think that it is probably wrong. Can anyone give me a counterexample?