Noetherian ring that isn't euclidean?
68633
Example of Noetherian ring over which the Euclidean algorithm is not valid.
69611
If $R$ and $S$ are rings then $R \times S$ is never a field
5594
Question about the Euclidean ring definition
26805
Non-Noetherian 0-dimensional ring
74314
Noetherian ring and the same prime divisors
46303
Example of a non-Noetherian complete local ring
17059
A ring element with a left inverse but no right inverse?
76749
Example of a finite non-commutative ring without a unity
4507
Localization of a ring which is not a domain
32741
Idempotents in a ring without unity (rng) and no zero divisors.
129858
"Almost" ring homomorphism
63192
A chain ring with Krull dimension greater than one
6646
A (non-artificial) example of a ring without maximal ideals
128861
If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated.
27823
Is the global section ring of a Noetherian Scheme Noetherian as well?
141100
Nontrivial subring with unity different from the whole ring?
85633
Rings of polynomials whose (partial) derivatives vanish are Noetherian?