Showing that in a well ordered ring homomorphic to $\mathbb{Z}$, there are no elements between zero and the ring's identity.
140868
Axiomatization of $\mathbb{Z}$ via well-ordering of positives.
123419
Abstract algebra: homomorphism and an element of a prime order
153291
Why a ring homomorphism from a local ring will not map a non-unit to a unit？
1577
Order of nontrivial elements is 2 implies Abelian group
5699
The number of ring homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
32741
Idempotents in a ring without unity (rng) and no zero divisors.
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
158426
Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
91962
In a ring $a*a=0$ then $a+a=0$
148616
When is a ring homomorphism $A \to A$ surjective but not injective.
75315
How to prove that homomorphism from field to ring is injective or zero?
24351
The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
155745
Ideals of $\mathbb{Z}[X]$
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
21840
Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$