Are there simple rings that are not division rings but have no zero divisors?
112560
Simple Noetherian domain which is not a division ring
114254
Zero divisors in $A[x_1,x_2,\dots,x_r]$
110726
Example of a non-gcd domain
114480
Example of a domain where all irreducibles are primes and that is not a GCD domain
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
45484
Height unmixed ideal and a non-zero divisor
30753
Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
151251
A simple algebra that is not semisimple
113512
Characteristic of nonzero commutative rings with unity
68807
How to show that the ring $S/A$ has no zero divisors? (Hungerford, Algebra, Problem 12, Chapter III, Section 2)
24203
Finding Zero Divisors and Units of Rings $\mathbb{Z}_n \times \mathbb{Z}_m$
1686
Show that quotient rings are not isomorphic
143051
Inverting noninvertible elements in a bigger ring.
79957
If $R$ is an infinite ring, then $R$ has either infinitely many zero divisors, or no zero divisors
120496
Examples of Non-Noetherian Valuation Rings
28688
why is a simple ring not semisimple?
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$