Ring $x^2=x$ then $2x=0$
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
116651
Show for any simple ring without identity, R, that R is a division ring.
148788
Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
74559
$A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.
98387
How to solve polynomial equations in a field and/or in a ring?
1141
Existence of totally ordered ring with zero divisors
14251
$P[X=x]=0$ when $X$ is continuous variable
157710
$x^{3}-x-2=0$ how do I find the roots?
105913
Calculations in quotient rings
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
116526
Finite ring has only zero divisors and units
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
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
26055
Multiplication by $0$ in a field
95146
Polynomial ring $R[X] $ has zero Jacobson radical, for $R$ a domain
23641
Quotient ring of field is zero or itself.
21840
Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$