Proof for maximal ideals in $\mathbb{Z}[x]$
37929
Classification of prime ideals of $\mathbb{Z}[X]$
45962
Show that any prime ideal from such a ring is maximal.
97605
Let $f$ be a surjective homomorphism. Prove that $\ker(f)$ is a maximal ideal
80397
Show that this set of polynomials is ideal in F[x]
121750
Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.
68202
Must an ideal generated by an irreducible element be a maximal ideal?
114343
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$
77903
Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
138026
To show that $n!f(x) \in \mathbb{Z}[x]$
131497
Maximal ideal not containing the set of powers of an element is prime
6307
maximal ideal not containing some expression
57198
How to show that a valuation ring has a unique maximal ideal?
87078
Prove the following set is an ideal of the ring $Z[x]$
93641
A maximal ideal among those avoiding a multiplicative set is prime
67203
Complement of maximal multiplicative set is a prime ideal
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number