Show that if, for the ring $(A, \bigtriangleup, \bot)$, $\bot^2x=x$ then $(A, \bigtriangleup, \bot)$ is a commutative ring
75520
If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.
109470
Proof of whether a specific element is in a commutative, invertible monoid.
5802
Proving the universal mapping property for polynomial rings
71822
Commutator algebra in exponents
97999
Explain these ring isomorphisms
30327
$\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
95806
Proving commutativity of convolution $(f \ast g)(x) = (g \ast f)(x)$
87946
Proving that the unities of a ring form a group under multiplication
119067
Basic Ring Theory Question involving the unit element
68732
Prove that a semigroup satisfying $a^pb^q=ba$ is commutative
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
88307
Commutative property of ring addition
108742
Proving commutativity of addition for vector spaces
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?
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
16023
Are associates unit multiples in a commutative ring with $1$?
56097
If $A$ and $AB-BA$ commute, show that $AB-BA$ is nilpotent