$h:X\to X$ endomorphism of module $X$ over $R$ satisfying $h\circ h = h$. Prove X = Im(h)\oplus Ker(h)
140314
A module as an external direct product of the kernel and image of an idempotent function
39576
Quotient ring being isomorphic to the initial ring
46664
Is every endomorphism of the quaternion ring surjective?
97605
Let $f$ be a surjective homomorphism. Prove that $\ker(f)$ is a maximal ideal
158583
Prove that if $M$ is an $R-$ projective left module then $M/IM$ is an $R/I-$ projective left module.
12104
How to prove this result involving the quotient maps and connectedness?
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
90010
Can we ascertain that there exists an epimorphism $G\rightarrow H$?
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
5802
Proving the universal mapping property for polynomial rings
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
122189
Show that $M[x]$ is a Noetherian $A[x]$-module.
70658
Isomorphism between quotient modules
93670
A surjective endomorphism (of a Noetherian ring) is injective.
1026
Ring homomorphism with $\phi(1_R) \neq1_S$
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}