# On the first and second Ext modules over some valuation rings

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 ?