Complement of a prime ideal is a subset closed under multiplication, containing 1
120149
Is the complement of a prime ideal closed under both addition and multiplication?
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
141687
Nonprincipal prime ideals contain two relatively prime elements
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
92519
ideal behind Maximal ideals are Prime ideals
6507
Every prime ideal of height 1 in a UFD is principal
20296
The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
116000
Prove that prime ideals of a finite ring are maximal
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
74558
Localization of ideals at all primes
52966
Rings, ideals and units-proof
138882
A prime poset of ideals
55764
Algebraic closure of $\mathbb F_p$
21946
What do prime ideals in $k[x,y]$ look like?
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
40162
Prove that the set $\mathbb{Q}[\alpha] = \{a+b\alpha+c\alpha^2 \mid a, b, c \in\mathbb{Q}\}$ is closed under addition and multiplication.