$1-r$ unit in ring with $r^n = 0$
22563
Units and Nilpotents
107821
The ring of integers of $\mathbf{Q}[i]$
114343
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$
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?
26805
Non-Noetherian 0-dimensional ring
52454
If $x^3 =x$ then $6x=0$ in a ring
70320
Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?
79535
Prove that $R$ is a commutative ring if $x^3=x$
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
16023
Are associates unit multiples in a commutative ring with $1$?
116526
Finite ring has only zero divisors and units
92822
Finite number of elements generating the unit ideal of a commutative ring
72507
Does $ab=1$ imply $ba=1$ in a ring?
37960
Zero Divisors in Direct Product of Rings
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
99715
Proper ideal and units proof
158311
What is the dimension of $R[[X]]$ where $R$ is a Noetherian ring?