  We prove that every positive trace on a countably generated *-algebra can be
approximated by positive traces on algebras of generic matrices. This implies
that every countably generated tracial *-algebra can be embedded into a metric
ultraproduct of generic matrix algebras. As a particular consequence, every
finite von Neumann algebra with separable pre-dual can be embedded into an
ultraproduct of tracial *-algebras, which as *-algebras embed into a
matrix-ring over a commutative algebra.
