My proof for $|R|=1$ if and only if $1=0$ where $R$ is a ring with unity.
66451
In a ring, how do we prove that a * 0 = 0?
48537
If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
87078
Prove the following set is an ideal of the ring $Z[x]$
72507
Does $ab=1$ imply $ba=1$ in a ring?
119067
Basic Ring Theory Question involving the unit element
147986
Prove: if $|z|=1$ than $\frac{z+1}{z-1}$ is an imaginary number
69012
How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?
67706
If $R$ is a Noetherian ring then $R[[x]]$ is also Noetherian
8317
Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
118873
Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
69353
Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$. Why would $R$ be finite?
18971
Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
152223
If $0<r<1$ show that $r^n$ goes to $0$ as $n$ goes to 1.
138632
Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$