Exercise in Atiyah's book: Prove that an ideal is prime.
107463
Is an ideal which is maximal with respect to the property that it consists of zero divisors necessarily prime?
19883
Prime ideals of the matrix ring
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
6699
An ideal that is maximal among non-finitely generated ideals is prime.
45962
Show that any prime ideal from such a ring is maximal.
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
27916
Are the determinantal ideals prime?
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
15904
Prime ideal and nilpotent elements
117536
Why is the localization at a prime ideal a local ring?
81743
Prime ideals in $C[0,1]$
252
Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
110984
Ideals and prime ideals in a commutative ring.
157876
If every prime ideal is maximal, what can we say about the ring?
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set