Show that a proper ideal I of a ring is equal to its own radical if and only it is an intersection of prime ideals
56800
Intersection of prime ideals
69373
Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
142863
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
103830
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
29019
Ideals in direct product of rings
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
40975
Quotient of the ring of integers of a number field by a prime ideal
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
110022
Showing prime and maximal ideal
37393
$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$
21946
What do prime ideals in $k[x,y]$ look like?
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