Can a ring without unity have a non-trivial subring with unity?
133738
Can a ring without a unit element have a subring with a unit element?
121008
A non-noetherian ring with all localizations noetherian
55900
Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
3037
Integral domain without unity has prime characteristic?
6646
A (non-artificial) example of a ring without maximal ideals
31451
Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
158426
Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
39755
In a faithfully flat ring extension, is $\operatorname{ht}I=\operatorname{ht}IS$ right?
93632
Existence of a ring homomorphism implies characteristic divisibility
107900
A ring which has many distinct left inverses
11938
What happens if we remove the requirement that $\langle R, + \rangle$ is abelian from the definition of a ring?
4507
Localization of a ring which is not a domain
76749
Example of a finite non-commutative ring without a unity
48480
Find two elements that don't have a gcd in a subring of Gaussian integers
137450
Two-sided ideal generated by subset of not commutative ring
149856
Image of ring homomorphism is a subring