Let $R$ be a ring, and let $C$={$x\in R: xy=yx$ for all y in $R$}
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
67470
If $S$ is a ring with the property that $s=s^2$ for each $s \in S$, then is $S$ commutative?
116883
About ideals in a ring which is a $k$ vector space
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
45523
Can the product of two non invertible elements in a ring be invertible?
145221
Ring isomorphism (polynomials in one variable)
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
156443
if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
122958
$R/I$ is commutative iff $rs-sr \in I$
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
79535
Prove that $R$ is a commutative ring if $x^3=x$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
29452
Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
138670
If product of finite elements in a ring is a unit then can we say each element as unit