Some algebraic properties of differential operators

First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield K((partial derivative(-1))) of pseudodifferential operators over K by the subalgebra K[partial derivative] 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 then we give an example of a 2 x 2 matrix with entries in A[partial derivative] whose Dieudonne determinant does not lie in A. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4720419]