Prime ideal and maximal ideal
45962
Show that any prime ideal from such a ring is maximal.
124151
Finite ring extension and number of maximal ideals
151829
Why are maximal ideals prime?
133975
Localising a polynomial ring and non-maximal prime ideal
138882
A prime poset of ideals
69352
Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
105313
Existence of minimal prime ideal contained in given prime ideal and containing a given subset
97740
Homogeneous ideals are contained in homogeneous prime ideals
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
145594
Splitting of prime ideals in algebraic extensions
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
112045
A property of minimal prime ideal
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
19883
Prime ideals of the matrix ring
97605
Let $f$ be a surjective homomorphism. Prove that $\ker(f)$ is a maximal ideal
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
62917
Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura