If in a ring $R$, $x^2=x$ for all $x$ then show that $2x=0$ and $x+y=0$ implies that $x=y$
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?
154495
Prove that a nontrivial subring of a ring that is a domain has the same identity
79535
Prove that $R$ is a commutative ring if $x^3=x$
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
83100
Prove that the center of a ring is a subring.
117590
Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal
119067
Basic Ring Theory Question involving the unit element
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
88051
$\mathbb R = X^2$ as a Cartesian product
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
16948
Need help with a proof that if $xy=0$ then $x=0$ or $y=0$
89702
Let $R$ be a ring such that for all $a,b$ in $R$, $(a^2-a)b=b(a^2-a)$. Then $R$ is commutative
52966
Rings, ideals and units-proof
41364
How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?