Finite ring has only zero divisors and units
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
4397
Finite rings without zero divisors are division rings.
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
18066
Prove that any non-zero-divisor of a finite dimensional algebra has an inverse
121663
If $a$ is a zero divisor of $\mathbb{F}$, then does $a$ fail to have a multiplicative inverse?
78350
When does a finite ring become a finite field?
153210
Why is every Noetherian zero-dimensional scheme finite discrete?
32772
Proving units in a ring
68807
How to show that the ring $S/A$ has no zero divisors? (Hungerford, Algebra, Problem 12, Chapter III, Section 2)
91962
In a ring $a*a=0$ then $a+a=0$
74314
Noetherian ring and the same prime divisors
92420
Characteristic of  a Non-unital Integral Ring
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
7303
How many idempotent elements does the ring ${\bf Z}_n$ contain?
37960
Zero Divisors in Direct Product of Rings
148550
Units in quotient ring of $\mathbb Z[X]$
69012
How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?