If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative
36996
If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
46863
Show that $g$ is injective
76661
Checking the maximality of a principal ideal in $R[x]$
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
156878
If every commutator is idempotent, then the ring is commutative
122958
$R/I$ is commutative iff $rs-sr \in I$
37393
$R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
101543
Let $A$ be a group, where $a^2=1$, a belongs to $A$. Prove that this group is commutative.
105471
How to prove that if each element of group is inverse to itself then group commutative?
18817
Does commutativity imply Associativity?
88307
Commutative property of ring addition
49527
Prove that $a$ commutes with each of its conjugates in $G$ iff $a$ belongs to an abelian normal subgroup of $G$.
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
94507
Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
52088
Isomorphism of an endomorphism ring, how can $R\cong R^2$?