  In the algebraic theory of algebra-valued noncommutative probability spaces,
for a unital algebra B, a mild reformulation of Speicher's noncrossing B-valued
cumulants for random variables in these spaces is used to construct canonical
random variables, acting on a Fock space over B, for arbitrary families of
B-valued random variables. Also, a condition for traciality of a trace on B
composed with the B-valued conditional expectation is given in terms of
B-valued cumulants.
