Prove for any ideal $J$, $\operatorname{rad} J$ is an ideal of $A$, if $J$ is ideal of $A$.
73417
$Rad(I)$ is an ideal of $R$
118513
Ideal of product of affine varieties
114343
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$
31585
Primary ideals of $\mathbb{Z}$
41629
Structure of ideals in the product of two rings
114193
On the absolute norm of an ideal
74559
$A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.
117786
Show that some monomial ideal is primary
104784
On the grade of an ideal
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
116883
About ideals in a ring which is a $k$ vector space
69352
Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
93658
Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
146801
Primary decomposition of an ideal
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
17239
Find all ideals of ${\mathbb{Z}_n}$