Suppose that we have a commutative ring $R$ and an exact sequence of graded R-modules $$0\rightarrow M'\rightarrow M\rightarrow M''\rightarrow 0$$ It is true that we have an exact sequence of graded R-modules $$0\rightarrow\text{S}^{\bullet}(M')\rightarrow\text{S}^{\bullet}(M)\rightarrow\text{S}^{\bullet}(M'')\rightarrow 0$$ where $\text{S}^{\bullet}(-)$ denotes the symmetric algebra?
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