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