Free $\oplus$ non-free $\cong$ free
82788
Direct summand of a free module
135422
$\operatorname{Hom}(-,A) \cong \operatorname{Hom}(-,A') \Rightarrow A \cong A'$, proof verification
40094
Does $G\oplus G \cong H\oplus H$ imply $G\cong H$ in general?
155799
What would be an example of free module such that cardinality of linearly independent set is greater than the rank?
27472
Prove that $PSL(2,\mathbb{Z})$ is free product of $C_2$ and $C_3$
91222
Isomorphism between $\mathfrak o(4,\mathbb R)$ and $\mathfrak o (3,\mathbb R) \oplus\mathfrak o (3,\mathbb R) $
148569
Embeddings $A → B → A$, but $A \not\cong B$?
156459
infinite monoid H that is not a free monoid and contains a free monoid as a submonoid
141802
Prove that free modules are projective
121361
Showing that $\lnot Q \lor (\lnot Q \land R) = \lnot Q$ without a truth table
18330
Does $R[x] \cong S[x]$ imply $R \cong S$?
18182
An abelian group $G$ with ${\rm Aut}(G)$ non-abelian
157202
$A\oplus C \cong B \oplus C$. Is $A \cong B$ when $C$ is finite, A and B infinite.
83109
Formation of the free group on $S$ is a functor
66806
A nonsplit short exact sequence of abelian groups with $B \cong A \oplus C$
150605
Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$
33868
A transformation between two free group actions.