Regular ring not UFD
94157
Normal Ring and Prime Ideal whose Square is Principal
32741
Idempotents in a ring without unity (rng) and no zero divisors.
46843
A ring without the Invariant Basis Number property
95902
Is this cylinder a regular surface?
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
116916
What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?
10866
What is difference between a ring and a field?
111679
Example of a ring without unity that has a subring with unity?
11541
Examples of a non-commutative division ring
75558
Counter-example for prime ideals in a non commutative ring.
143051
Inverting noninvertible elements in a bigger ring.
85915
Principal prime ideals are minimal among prime ideals in a UFD
24351
The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
78350
When does a finite ring become a finite field?
105887
Ring and Subring with different Identities
51974
Does the Bezout GCD equation hold in a UFD?
131319
I understand what a division ring is, but cannot find any examples. Can anyone give me one?