  An abelian self-commutator in a C*-algebra $\mathcal{A}$ is an element $A$
that can be written as $A=X^*X-XX^*$, with $X\in\mathcal{A}$ such that $X^*X$
and $XX^*$ commute. It is shown that, given a finite AW*-factor $\mathcal{A}$,
there exists another finite AW*-factor $\mathcal{M}$ of same type as
$\mathcal{A}$, that contains $\mathcal{A}$ as an AW*-subfactor, such that any
self-adjoint element $X\in\mathcal{M}$ of quasitrace zero is an abelian
self-commutator in $\mathcal{M}$.
