If $0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0$ is exact and $B\simeq A\oplus C$ as a $R$-module, does this sequence split?
66806
A nonsplit short exact sequence of abelian groups with $B \cong A \oplus C$
7708
Obstruction to the splitness of an exact sequence of holomorphic vector bundles
37570
$M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
76674
Let $S:U\rightarrow V, \ T:V\rightarrow W$ and if $S$ and $T$ are both injective/surjective, is $T\circ S$ injective/surjective?
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
134294
A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$.
1026
Ring homomorphism with $\phi(1_R) \neq1_S$
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
127488
If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
29600
What is true for a ring with exactly two right ideals
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
53335
Why isn't $\mathbb{C}[x,y,z]/(xz-y)$ a flat $\mathbb{C}[x,y]$-module
36987
A criterion of flat modules
134384
What does $\rightarrow$ mean in $p \rightarrow q$
14688
Do sequences in $\ell^p$ belong to some $\ell^q$ for $q<p$?
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
144105
Ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is always identity or $0$