Tagged Questions
8
votes
1answer
305 views
Does the splitting lemma hold without the axiom of choice?
In part of the proof of the splitting lemma (a left-split short exact sequence of abelian groups is right-split) it seems necessary to invoke the axiom of choice. That is, if $0\to A\overset{f}{\to} ...
3
votes
4answers
176 views
$F$ is a free abelian group on a set $X$ , $H \subseteq F$ is a free abelian group on $Y$, then $|Y| \leq |X|$
I am confused by the proof a proposition:
$F$ is a free abelian group on a set $X$ and $H$ is a subgroup of $F$, then $H$ is free abelian on a set $Y$, where $|Y| \leq |X|.$
The proof is:
...
