Incorrect Proof for $x^3 = x$ for every $x$ in a ring $R$ then R is commutative.
75520
If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.
92962
Rings with $a^5=a$ are commutative
74559
$A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.
133878
Ring of order $p^2$ is commutative.
18971
Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
124564
Prove the ring $a+b\sqrt[3]{2}+c\sqrt[3]{4}$ has inverse and is a field
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
96153
$ x^3<y^3 \iff x<y $ proof issue.
44405
Prove XOR is commutative and associative?
22604
Can $R \times R$ be isomorphic to $R$ as rings?
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
41398
For a ring $R$, does $\operatorname{End}_R(R)\cong R^{\mathrm{op}}$?
26764
Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
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?
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$