Idempotent endomorphism: show $M=\text{Range}(f) \oplus \text{Range}(\text{id} - f)$
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
47630
Endomorphisms of modules satisfying chain conditions and counterexamples.
8417
Natural $(R/I)$-module structure for an $R$-module $M$ annihilated by $I$
152721
Help showing $H_n=\sum_{h \in H}h \in F[H]$ is a simple submodule
84301
Showing that some Function on the Unit Disc is injective
111191
Show that $P_i$ and $\sum_i P_i$ being idempotent implies $P_i P_j=\delta_{ij}$
65977
Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
72350
Constructing Idempotent Generator of Idempotent Ideal
30178
Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
118354
Epimorphism and Monomorphism = Isomorphism?
5635
How to prove that the Frobenius endomorphism is surjective?
91736
Explicit homeomorphism between open and closed rational intervals?
3682
If $V = \text{null}(\textsf{T}-\lambda\textsf{I}) \oplus \text{range}(\textsf{T}-\lambda\textsf{I})$, then prove that $\textsf{T}$ is diagonalizable
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
41895
Show $\text{Hom}_{Ab}(A,\mathbb{Q}) = \{0\}$ for finite $A$
15175
When does a Möbius transformation map $\Im(z)>0$ to itself?
27757
$\mathbb{R}\to\mathbb{R}$ Diffeomorphism with special property