$x^n=x$ implies commutativity in rings
79535
Prove that $R$ is a commutative ring if $x^3=x$
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
97608
Showing a Ring of endomorphisms is isomorphic to a Ring
32772
Proving units in a ring
23521
Power Set of $X$ is a Ring with Symmetric Difference, and Intersection
157585
Structure theorem of finite rings
39576
Quotient ring being isomorphic to the initial ring
110984
Ideals and prime ideals in a commutative ring.
151993
Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
133878
Ring of order $p^2$ is commutative.
30327
$\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
27766
Comaximal ideals in a commutative ring
108742
Proving commutativity of addition for vector spaces
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
26661
Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
18817
Does commutativity imply Associativity?
151803
Prove that $R$ is commutative