Give an example of an ideal that is not a subring, and a subring that is not an ideal.
65091
Subring which is not an ideal?
6646
A (non-artificial) example of a ring without maximal ideals
28327
(Simple) Examples on Non-Commutative Rings
140553
An ideal which is not finitely generated
45484
Height unmixed ideal and a non-zero divisor
8587
What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
131497
Maximal ideal not containing the set of powers of an element is prime
87382
Non-invertible elements form an ideal
137450
Two-sided ideal generated by subset of not commutative ring
20296
The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
33576
Non-principal ideal in $K[x,y]$?
148569
Embeddings $A → B → A$, but $A \not\cong B$?
150170
Subrings of fraction fields
19996
Example where union of increasing sigma algebras is not a sigma algebra
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
93358
Find an example of a non-surjective field endomorphism