Polynomial ring
Properties
Prime ideals
If $R$ is a Principal ideal domain, then the prime ideals of $R[y]$ are of the following form:
- $(0)$
- $(f(y))$ where $f$ is irreducible
- $(p,f(y))$ where $p\in R$ is prime and $f(y)$ is irreducible in $(R/p)[y]$. (see answer at https://math.stackexchange.com/questions/56916/what-do-prime-ideals-in-kx-y-look-like)
Graded ring structure
(See Graded ring for definitions and properties of graded rings.)
Letting
\begin{gather}
S=k[x_0,\dots,x_n],\
S_d = {}
\end{gather}