Maximal ideals in rings of polynomials Let $k$ be a field and $D = k[X_1, . . . , X_n]$ the polynomial ring in $n$ variables over $k$.
Show that:
a) Every maximal ideal of $D$ is generated by $n$ elements.
b) If $R$ is ring and $\mathfrak m\subset D=R[X_1,\dots,X_n]$ is maximal ideal such that $\mathfrak m \cap R$ is maximal and generated by $s$ elements, then $\mathfrak m$ is generated by $s + n$ elements.
The days that I am trying to solve. Help me.

The answer to question a) can be found as Corollary 12.17 in these (Commutative Algebra) notes.  The proof is left as an exercise, but the proof of it is just collecting together the previous results in the section.
(As Patrick DaSilva has mentioned, as written your question b) follows trivially from part a).  I'm guessing it's not what you meant to ask.)
