why prime ideal and maximal ideal are same in finite integral domain?
38228
Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.
116430
If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
129371
Maximal ideals in the ring of real functions on $[0,1]$
81982
Is $\mathbb{Z}[x]$ a principal ideal domain?
90889
Prime ideals in a finite direct product of rings
138572
Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?
119056
If in a UFD every maximal ideal is principal then it is a PID
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
17247
Localisation and prime ideals
45962
Show that any prime ideal from such a ring is maximal.
112045
A property of minimal prime ideal
67669
Prime ideals of a finite direct product ring
46040
Preimage of maximal ideal is maximal (why is this answer wrong?)
6307
maximal ideal not containing some expression
29126
Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
67342
Why does a minimal prime ideal consist of zerodivisors?
74537
Maximal Ideals in $K[y]$