Prove $R$ is commutative if $x^2=x$ for every $x\in R$.
2709
How to show that every Boolean ring is commutative?
69875
Prove the commutativity property of addition of natural numbers by induction
108742
Proving commutativity of addition for vector spaces
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
115583
prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
95806
Proving commutativity of convolution $(f \ast g)(x) = (g \ast f)(x)$
111493
Division algorithm for polynomials in R[x], where R is a commutative ring with unity.
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
75520
If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.
99662
proving than every $2\times 2$ is similar to a united form
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
43990
R is a commutative ring with $1\ne 0$ and $R^m \cong R^n$, then $m=n$
43020
If $I+J=R$, where $R$ is a commutative rng, prove that $IJ=I\cap J$.
32155
Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
10254
Is the Polynomial Factor Theorem true over all commutative rings?
103932
How can I prove that a polynomial with degree $n$ is continuous everywhere in $\mathbb{R}$ using definitions?
45811
How to prove that r is a double root if and only if it is a root of a polynomial and of its derivative.