Injective homomorphism $R^n\rightarrow R^m$ implies $n\leq m$?
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
11202
If $g \circ f$ is injective, so is $g$
67199
Isomorphism $H_n(D^n, S^{n - 1};A)$ and $A$
90010
Can we ascertain that there exists an epimorphism $G\rightarrow H$?
157378
On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
7938
Number of Homomorphisms from $\Bbb{Z}_m$ to $\Bbb{Z}_n$
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
151354
Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?
28692
Find if set $I$ of all injective functions $\mathbb{N} \rightarrow \mathbb{N}$ is equinumerous to $\mathbb{R}$
51334
Does there exist any surjective group homomorphism from $(\mathbb R^* , .)$ onto $(\mathbb Q^* , .)$?
121244
Homomorphisms and automorphisms on polynomial rings
46355
If $[G:H]=n$, is it true that $x^n\in H$ for all $x\in G$?
101064
Showing the triviality of homomorphisms
95086
Homeomorphism is bijective
47709
If $n\mid m$ prove that the canonical surjection $\pi: \mathbb Z_m \rightarrow \mathbb Z_n$ is also surjective on units
51695
Finding all homomorphisms between $\mathbb{Z}/m\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$