A ring is never a direct sum of infinitely many non-zero left ideals?
39049
Ring With Unity As a Direct Sum of Non-Zero 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.
80679
Principal ideal rings that are not integral domains
24351
The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
141100
Nontrivial subring with unity different from the whole ring?
67342
Why does a minimal prime ideal consist of zerodivisors?
52966
Rings, ideals and units-proof
66451
In a ring, how do we prove that a * 0 = 0?
107454
Why D/I is finite if I is a non-zero ideal of the ring of integers of a number field?
124151
Finite ring extension and number of maximal ideals
21604
A complete ring with respect to an ideal
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
45484
Height unmixed ideal and a non-zero divisor
114640
Showing that an ideal is not a free $R-$module.
101095
Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
91962
In a ring $a*a=0$ then $a+a=0$
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$