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 Let R be a ring with 1 and M a left R-module

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 Let R be a ring with 1 and M a left R-module. If N is a submodule of M, the annihilator of N in R is defined to be:
{r in R/rn=0 for all n in N}

Prove that the annihilator of N in R is a two-sided ideal of R.