If $a^2=a\enspace\forall~a\in R$, then the ring $R$ is commutative
67470
If $S$ is a ring with the property that $s=s^2$ for each $s \in S$, then is $S$ commutative?
41398
For a ring $R$, does $\operatorname{End}_R(R)\cong R^{\mathrm{op}}$?
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
138309
Ring whose all ideals are double-sided is commutative?
66968
if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent
151803
Prove that $R$ is commutative
52966
Rings, ideals and units-proof
79897
if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian
35777
$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
158311
What is the dimension of $R[[X]]$ where $R$ is a Noetherian ring?
27766
Comaximal ideals in a commutative ring
65224
Prove that if $a^2 = a$ for all elements of the ring $R$, then $R$ has characteristic 2. Is the converse of the statement true?
79535
Prove that $R$ is a commutative ring if $x^3=x$
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
50212
$R/Ra$ is an injective module over itself
25764
Example of a ring such that $R^2\simeq R^3$, but $R\not\simeq R^2$ (as $R$-modules)
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?