#### M. Lorenz, Z. Reichstein, * Lattices and parameter reduction in
division algebras *, January 2000.

**Abstract:** Let *k* be an algebraically closed field
of characteristic
0 and let *D* be a division algebra

whose center *F* contains *k*. We shall say that *D*
can be reduced to *r* parameters if we can write

*D* =
*D*_{0} tensor _{F0}
*F*, where *D*_{0} is a division algebra, the center
*F*_{0} of *D*_{0} contains *k* and trdeg_{k}(*F*_{0})
=* r*.

We show that every division algebra of odd degree * n *
can be reduced to
<= ^{1}/_{2}(*n*-1)(*n*-2)

parameters. Moreover, every crossed product division algebra of degree
n >= 4 can be reduced to <= ([log_{2}(*n*)] -1)
*n* + 1 parameters.

Our proofs of these results rely on lattice-theoretic techniques.

Postscript file

DVI file