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Let $R$ be an integral domain with the quotient field $K$.

Let $M$ be a finitely generated $R$-submodule in $K^n$.

Is it true that $M$ is free $R$-module?

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    Well, it seems to be that nice implies integral domain, which is a rather heavy assumption for a (general) ring: unitary, commutative without non-trivial zero divisors.2012-10-07
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    I just need to work in integral domain. Is this statement true?2012-10-07
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    Your question is true if there exists a unique homomorphism $\hat f:M\to N $ such that $\hat f \circ i= f:S \to N$, where $S$ is a set and $i$ is a set map $i: S \to M$.2012-10-07

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