Ring of rational 2x2 matrices has no proper ideals
38817
Why is the ring of matrices over a field simple?
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
135781
Division ring if and only if it has no proper left ideals.
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.
24203
Finding Zero Divisors and Units of Rings $\mathbb{Z}_n \times \mathbb{Z}_m$
133495
Example of a ring without Invariant Basis Property
37960
Zero Divisors in Direct Product of Rings
133975
Localising a polynomial ring and non-maximal prime ideal
17991
Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
22610
Polynomial rings in infinitely indeterminants
127030
Simple example of non-arithmetic ring (non-distributive ideal lattice)
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
151251
A simple algebra that is not semisimple
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
116526
Finite ring has only zero divisors and units
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
124864
A not free $\mathbb{Z}$-module