How do I prove that the standard definition of prime ideal is equivalent to that of Krull's?
72230
Equivalence of definitions of prime ideal in commutative ring
73095
Foundational proof for Mersenne primes
135682
Are distinct prime ideals in a ring always coprime? If not, then when are they?
93641
A maximal ideal among those avoiding a multiplicative set is prime
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
158106
Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
117536
Why is the localization at a prime ideal a local ring?
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
58425
Defining the Product of Ideals
137715
If $[L:K]$ is prime, show that $L/K$ is a simple extension.
107463
Is an ideal which is maximal with respect to the property that it consists of zero divisors necessarily prime?
75558
Counter-example for prime ideals in a non commutative ring.
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
34183
An equivalent condition with $\{0\}$ being the only nilpotent ideal
6699
An ideal that is maximal among non-finitely generated ideals is prime.
110022
Showing prime and maximal ideal
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )