Differences between ideal and subalgebra

422 Views Asked by At

Let $ R=K[x]$ be the polynomial ring over the field $K$ and $S=\{x^4+x^3 , x^2+x\} \subset R$. If $I$ be the ideal generated by $S$ and $B$ be a subalgebra of $R$ generated by $S$, can someone please explain their differences. What would be the elements of $B$?