Some algebraic properties of differential operators
  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. 
Sylvain Carpentier, Alberto De Sole and Victor G. Kac
math.RA math-ph math.MP nlin.SI