  The commutative algebra of functions on a manifold is extended to a
noncommutative algebra by considering its tensor product with the algebra of
nxn complex matrices. Noncommutative geometry is used to formulate an extension
of the Einstein-Hilbert action. The result is shown to be equivalent to the
usual Kaluza-Klein theory with the manifold SUn as an internal space, in a
truncated approximation.
