Explain why J is a prime Ideal in Z[x]
98587
$\mathbb Z [X] / (X)$ isomorphic to $\mathbb Z[X] / (X+1)$ isomorphic to $\mathbb Z [X] / (X+2015)$
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
81743
Prime ideals in $C[0,1]$
112045
A property of minimal prime ideal
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
27916
Are the determinantal ideals prime?
116430
If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
46383
If $x$ divides $z$, $y$ divides $z$ and $x$ and $y$ are relatively prime, then $xy$ divides $z$.
103518
If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
121986
Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
23099
Verifying that the ideal $(x^3-y^2)$ is prime
147871
How do the prime ideals of $\mathbb{Z}_{k}$ look like?
69710
Is it true that an ideal is primary iff its radical is prime?
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
93641
A maximal ideal among those avoiding a multiplicative set is prime