$R$ a commutative ring, $I$ a f.g. ideal and $I^2=I$ $\implies$ $I=Re$ for some idempotent element
60674
Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
7303
How many idempotent elements does the ring ${\bf Z}_n$ contain?
99715
Proper ideal and units proof
138130
If $I$ is a maximal ideal of $R$, why is $R/I$ a field?
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
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 $R$
52966
Rings, ideals and units-proof
118781
product of ideals in matrix ring
47134
Ideals generated by two elements
50908
Showing a Ring and an Ideal are equal
56278
$I$ and $J$ are coprime ideals iff $x \to (x + I, x + J)$ is surjective.
122958
$R/I$ is commutative iff $rs-sr \in I$
63171
Translate of an ideal by $a$ coincides with the ideal iff  $a \in I$
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
24259
Quotient ring of $T/I$
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