Theorem 17.5 Gallian: A polynomial generates a maximal ideal if and only if it is irreducible.
93658
Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
140808
Problem on Galois theory and irreducible polynomial
118306
$I:=\{f(x)\in R\mid f(1)=0\}$ is a maximal ideal?
134991
Commutative non Noetherian rings in which all maximal ideals are finitely generated
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
6699
An ideal that is maximal among non-finitely generated ideals is prime.
140553
An ideal which is not finitely generated
54916
Maximal ideal in commutative ring
80397
Show that this set of polynomials is ideal in F[x]
28244
Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal?
133975
Localising a polynomial ring and non-maximal prime ideal
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
22716
$A$ is integrally closed if and only if $A_P$ is integrally closed for all maximal ideals $P$ of $A$.
104486
Ideal in $\mathbb Z[x]$ which is not two-generated
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?