Existence of injective homomorhism and surjective homomorphism of free modules implies isomorphism
130464
Exercise 2.11 Atiyah-Macdonald
61491
Complex Ring Isomorphism
127044
Prove that a finitely-generated free module has a finite basis
50212
$R/Ra$ is an injective module over itself
82689
Monos in $\mathsf{Mon}$ are injective homomorphisms.
129162
Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
88930
Homomorphism between free groups
93632
Existence of a ring homomorphism implies characteristic divisibility
110808
Isomorphisms preserve cyclic
45792
Rigorous proof that surjectivity implies injectivity for finite sets
37058
Induced maps in homology are injective
128493
Given a commutative ring $R$ and an epimorphism of free modules $R^m \to R^n$ is then $m \geq n$?
9562
Proving that surjective endomorphisms of Noetherian modules are isomorphisms and a semi-simple and noetherian module is artinian.
30714
A question on ring homomorphisms and maximal ideals.
30236
isomorphic groups related in direct product.
148616
When is a ring homomorphism $A \to A$ surjective but not injective.
99707
free module implies surjective map of affine schemes