There is no endomorphism $\phi : \mathbb R^5 \to \mathbb R^5$ with $\ker \phi = \text{Im}\phi$
121244
Homomorphisms and automorphisms on polynomial rings
98696
Is the exponential map ever not injective?
30327
$\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
105333
Generated $\sigma$-algebras with cylinder set doesn't contain the space of continuous functions
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
102299
Bijection between $\mathbb{R}^n$ and $\mathbb{R}^m$
99884
Are $\mathbb{Q}_p$ and $\mathbb{Q}_q$ homeomorphic?
126472
Surjective endomorphisms of uniserial modules
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
109987
No homomorphism from $Z_{16}\oplus Z_{2}$ onto $Z_{4}\oplus Z_{4}$.
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
9562
Proving that surjective endomorphisms of Noetherian modules are isomorphisms and a semi-simple and noetherian module is artinian.
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
111689
Surjective, but not injective endomorphism
155266
Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?