%0 Journal Article
%T Some algebraic properties of differential operators
%A Sylvain Carpentier
%A Alberto De Sole
%A Victor G. Kac
%J Physics
%D 2012
%I arXiv
%R 10.1063/1.4720419
%X 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.
%U http://arxiv.org/abs/1201.1992v1