Suppose $k$ is a field and $k[x]$ the ring of polynomials in one variable with coefficients in $k$. Is there any classification theorem that tells us what a subring of $k[x]$ will look like? I can think of specific examples of subrings (such as the polynomials with $f'(0)=0$) but I know there are examples that show that a subring doesn't even have to be Noetherian, so I wonder what is known in general about a subring of $k[x]$.
1
- 1$\begingroup$ Various bits of informationa are to be found in e.g. math.stackexchange.com/q/4493489/96384, math.stackexchange.com/q/673369/96384, math.stackexchange.com/q/3138215/96384, and further links form there. $\endgroup$Torsten Schoeneberg– Torsten Schoeneberg2022-07-19 04:53:57 +00:00Commented Jul 19, 2022 at 4:53
Add a comment |