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!