An example of a ring without identity that does not contain any maximal ideal.
6646
A (non-artificial) example of a ring without maximal ideals
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
30753
Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
100340
Invariant dimension property on a ring without zero divisors
46843
A ring without the Invariant Basis Number property
68807
How to show that the ring $S/A$ has no zero divisors? (Hungerford, Algebra, Problem 12, Chapter III, Section 2)
36078
Example of a non invertible fractional ideal
116651
Show for any simple ring without identity, R, that R is a division ring.
45971
Complete local ring which is not complete valuation ring
143884
A non-noetherian ring with noetherian spectrum
114329
Example of subring that is not an ideal
17991
Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
34203
if $S$ is a ring (possibly without identity) with no proper left ideals, then either $S^2=0$ or $S$ is a division ring.
30465
Determining which rings have a module which is not semisimple
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
10943
What is an example of a radical of sum of ideals not being equal to the sum of radicals?
6307
maximal ideal not containing some expression