Prove that if $I$ is a right ideal of $R$ and $I$ is a direct summand of $R$ then $I=eR$ for some idempotent $e \in R$
64484
Left ideal $I$ is a direct summand of $R$ iff $I = Rr$, $r^2 = r$
102112
Idempotents in $\mathbb Z_n$
24259
Quotient ring of $T/I$
43889
Prove that $u-i$ is a maximal ideal of $\frac {\Bbb C[X,Y]} {\left (X^2+Y^2-1 \right )}.$
21604
A complete ring with respect to an ideal
111307
If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.
103349
A question about a proof of Noetherian modules and exact sequences
157605
$IS \mid JS$ implies that $I\mid J$ where $I$ and $J$ are ideals of a number ring contained in another number ring $S$
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
112045
A property of minimal prime ideal
81296
If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
151803
Prove that $R$ is commutative
17895
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
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
15320
Morita equivalence and right and left ideals of a Ring
50114
A question about direct sums and products of modules
29600
What is true for a ring with exactly two right ideals