Is there an infinite ring having finitely many zero divisors?
79957
If $R$ is an infinite ring, then $R$ has either infinitely many zero divisors, or no zero divisors
80616
A ring with few invertible elements
112910
Is the set of real numbers really uncountably infinite?
51428
Do these two observations suffice to show that a finite boolean ring must be of the form $\mathbb{Z}_2\times\cdots\times\mathbb{Z}_2$?
133738
Can a ring without a unit element have a subring with a unit element?
100340
Invariant dimension property on a ring without zero divisors
4397
Finite rings without zero divisors are division rings.
150605
Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$
124151
Finite ring extension and number of maximal ideals
22610
Polynomial rings in infinitely indeterminants
16643
A slick proof that a field which is finitely generated as a ring is finite
134991
Commutative non Noetherian rings in which all maximal ideals are finitely generated
84751
How can it be possible to localize a ring at a set with zero divisors?
84149
Prove that an infinite ring with finite quotient rings is an integral domain
138469
Is a ring of integers necessarily Noetherian?
111679
Example of a ring without unity that has a subring with unity?
14055
How to show that a finite commutative ring without zero divisors is a field?