Show that each of the ideals $I_k=\langle x_1,...,x_k\rangle$ in $F[x_1,...,x_n]$ for $1\leq k \leq n$ are prime and that each power is primary
113002
Any power of $(X_1, X_2,...,X_i)$ is primary in $k[X_1, X_2,...,X_n].$
89782
To show that $\langle x-a , y-b\rangle$ is a maximal ideal of $F[x,y]$ by showing that $F[x,y]/\langle x-a , y-b\rangle$ is a field
20296
The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
102341
Primary decomposition of a monomial ideal
117786
Show that some monomial ideal is primary
85915
Principal prime ideals are minimal among prime ideals in a UFD
37929
Classification of prime ideals of $\mathbb{Z}[X]$
87103
Quick question about ideals of field $F$ in $F[x]$ are principal.
112045
A property of minimal prime ideal
92519
ideal behind Maximal ideals are Prime ideals
63447
Prove that the kernel of a homomorphism is a principal ideal. (Artin, Exercise 9.13)
1719
Ideals in the ring of Gaussian integers
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
49875
Question on Comaximal Ideals
108767
Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
116883
About ideals in a ring which is a $k$ vector space
87078
Prove the following set is an ideal of the ring $Z[x]$