Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R$. Prove that if $I$ is prime then $R/I$ is an integral domain.
74370
$P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$
94819
Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.
112099
Polynomial ring with integral coefficients is integral
31049
If $p$ is an irreducible element of an integral domain $D$, and if $e$ belongs to $D^\ast$ prove that $ep$ is also ireducible
154239
Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
84149
Prove that an infinite ring with finite quotient rings is an integral domain
5360
Ideal contained in a finite union of prime ideals
19883
Prime ideals of the matrix ring
111996
Maximal and Prime Ideal in Z
15137
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
62951
Is there a more direct way of proving that this ring is an integral domain?
81743
Prime ideals in $C[0,1]$
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
54916
Maximal ideal in commutative ring
62917
Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
111307
If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.