Every maximal ideal is a prime ideal
92071
A maximal ideal is always a prime ideal?
138882
A prime poset of ideals
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
19883
Prime ideals of the matrix ring
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
135586
Prove that the preimage of a prime ideal is also prime.
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
137675
Every proper ideal is contained in a maximal ideal, in a commutative ring with identity.
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
111996
Maximal and Prime Ideal in Z
37929
Classification of prime ideals of $\mathbb{Z}[X]$
29126
Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
30714
A question on ring homomorphisms and maximal ideals.
38228
Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.