  First, we study the subskewfield of rational pseudodifferential operators
over a differential field K generated in the skewfield of pseudodifferential
operators over K by the subalgebra of all differential operators.
  Second, we show that the Dieudonne' determinant of a matrix
pseudodifferential operator with coefficients in a differential subring A of K
lies in the integral closure of A in K, and we give an example of a 2x2 matrix
differential operator with coefficients in A whose Dieudonne' determiant does
not lie in A.
