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I want to know what the "one-sided" (say, left)) ideals of the polynomial ring $R[x]$ are, as to obtain the left socle of this ring.

If $I$ is a left ideal of $R$, then $I[x]$ comprising all polynomials with the coefficients in $I$ is necessarily a left ideal of $R[x]$. But, as for the left ideals, ..., I didn't reach any.

Thanks to any help!

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    This is probably more suitable for MSE, but the left socle is zero, as there are no simple left ideals: if $S$ is any non-zero left ideal, then $xS$ is a proper non-zero subideal of $S$. – 2017-01-28

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