$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$
43020
If $I+J=R$, where $R$ is a commutative rng, prove that $IJ=I\cap J$.
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
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
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
85913
R is commutative ring with identity & define $\circ$ on $R$ by for any $a,b \in R$ $a \circ b=a+b-ab$ Prove the following
50908
Showing a Ring and an Ideal are equal
50445
Explaining the product of two ideals
74796
Extension of intersection of ideals
21604
A complete ring with respect to an ideal
87078
Prove the following set is an ideal of the ring $Z[x]$
124646
Understanding the ideal $IJ$ in $R$
99715
Proper ideal and units proof
138752
Prove the Radical of an Ideal is an Ideal
29019
Ideals in direct product of rings
126672
Product of principal ideals: $(a)\cdot (b) = (a b)$
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
62711
Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism