Every Ideal of the ring $R \times S$ (where R and S are rings) is the cartesian product of the ideals $J_1 \subseteq R$ and $J_2 \subseteq S$
41629
Structure of ideals in the product of two rings
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 $R$
81296
If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
49875
Question on Comaximal Ideals
155745
Ideals of $\mathbb{Z}[X]$
54345
Prove if a non-trivial ring $R$ has a unique maximal left ideal $J$ , then $J$ is two-sided and is also the unique maximal right ideal in $R$.
22604
Can $R \times R$ be isomorphic to $R$ as rings?
141683
$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
54916
Maximal ideal in commutative ring
69611
If $R$ and $S$ are rings then $R \times S$ is never a field
15320
Morita equivalence and right and left ideals of a Ring
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
87151
Primary ideals in Noetherian rings
108807
Subset of a cartesian product
140865
Rings' second isomorphism theorem