$J \neq 0$ ideal in $R=\mathbb{Z}[i]$. show that $J \cap \mathbb{Z}$ is an ideal in $\mathbb{Z}$
138168
Prove: The pre-image of an ideal is an ideal.
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 $\mathbb Z$?
23392
The annihilator of a module is an ideal
146801
Primary decomposition of an ideal
96787
Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?
15137
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
148208
In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I),P=I:a$ for some $a\in R$.
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
31585
Primary ideals of $\mathbb{Z}$
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
90314
Maximal ideals in $R[x]$
117590
Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal
5360
Ideal contained in a finite union of prime ideals
58640
$R$ is an algebra over an infinite field. If $\exists$ ideals s.t. $J\subseteq \bigcup_{k=1}^nI_k$ then $J\subseteq I_k$ for some $k$
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
17075
Show an Ideal is the principal ideal for some polynomial.
147871
How do the prime ideals of $\mathbb{Z}_{k}$ look like?