Let R be a ring. Prove that if $x^2=x$ for each $x \in R$, then R is a commutative ring.
2709
How to show that every Boolean ring is commutative?
151803
Prove that $R$ is commutative
119067
Basic Ring Theory Question involving the unit element
121750
Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.
80232
Suppose that R is a commutative ring with unity such that for each $a$ in $R$ there is an integer $n > 1\mid a^n =a$. Every prime ideal is maximal?
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
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
1315
Let $R$ be a ring. Define a circle composition ◦ in R by $a ◦ b =a+b-ab$, $a, b ∈ R$.
81296
If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
138826
To show that either $R$ is a field or $R$ is a finite ring with prime number of elements and $ab = 0$ for all $a,b \in R$.
133878
Ring of order $p^2$ is commutative.
44405
Prove XOR is commutative and associative?
111493
Division algorithm for polynomials in R[x], where R is a commutative ring with unity.
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
48537
If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative
144442
Let $R$ be a commutative unital ring. Is it true that the group of units of $R$ is not isomorphic with the additive group of $R$?