prove that in $k[x_1,...,x_n]$ Ideal of polynomials vanishing on some $(a_1,a_2,...,a_n)$ will be $\langle x_1-a_1,...,x_2-a_2\rangle$.
30327
$\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
58425
Defining the Product of Ideals
116883
About ideals in a ring which is a $k$ vector space
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
88466
Show that polynomial $X^{n+1}-aX^n+aX-1$ has only roots of module $1$
95031
Find generators of the ideal of an algebraic set
77820
Roots in a polynomial ring
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
17075
Show an Ideal is the principal ideal for some polynomial.
49875
Question on Comaximal Ideals
18036
Localization by a non-nilpotent as a polynomial quotient
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
124460
Show that if $f \in \mathbb{C} \left[x_1, \dots, x_n \right]$ vanishes at every point of $\mathbb{Z}^n$, then $f$ is the zero polynomial.
74537
Maximal Ideals in $K[y]$
48873
Let $K$ be a field and $f(x)\in K[X]$ be a polynomial of degree $n$. And let $F$ be its splitting field. Show that $[F:K]$ divides $n!$.
31585
Primary ideals of $\mathbb{Z}$
112043
Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal