Maximal element of a subset of ideals is often prime
138882
A prime poset of ideals
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
90889
Prime ideals in a finite direct product of rings
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
141687
Nonprincipal prime ideals contain two relatively prime elements
89313
Maximal ideals of polynomial rings in infinitely many variables
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
34807
Localization at finitely many minimal prime ideals
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree
93658
Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
108896
Prime ideal in a polynomial ring over an integrally closed domain
135586
Prove that the preimage of a prime ideal is also prime.
56800
Intersection of prime ideals
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
154239
Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?