$R$ is commutative ring with unity, prove $I,J\trianglelefteq R \wedge I+J=R \Rightarrow IJ=I\cap J$
37393
$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$
133878
Ring of order $p^2$ is commutative.
107821
The ring of integers of $\mathbf{Q}[i]$
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
57031
Ring of fractions of $R$ is integral over $R$
111493
Division algorithm for polynomials in R[x], where R is a commutative ring with unity.
6896
If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$
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
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 $R$.
121750
Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.
83100
Prove that the center of a ring is a subring.
118781
product of ideals in matrix ring
156878
If every commutator is idempotent, then the ring is commutative
124646
Understanding the ideal $IJ$ in $R$
108742
Proving commutativity of addition for vector spaces
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$