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Let $(R, \mathfrak m)$ be a valuation ring of finite Krull dimension, with non-principal maximal ideal. So that $\mathfrak m^2=\mathfrak m$.

If $M$ is an $R$-module with $Supp M=\{ \mathfrak m \}$ , then is it true that either $Ext^1_R (R/ \mathfrak m, M)$ or $Ext^2_R (R/ \mathfrak m, M)$ is zero module ?

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