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((∂⁻¹)) of pseudodifferential operators over K by the subalgebra K[∂] of all differential operators. Second, we show that the Dieudonnè determinant of a matrix pseudodiff...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
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AIP Publishing
2018
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| Online Access: | http://hdl.handle.net/1721.1/115839 https://orcid.org/0000-0001-6809-4128 https://orcid.org/0000-0002-2860-7811 |
| Summary: | First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield K((∂⁻¹)) of pseudodifferential operators over K by the subalgebra K[∂] of all differential operators. Second, we show that the Dieudonnè 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 × 2 matrix with entries in A[∂] whose Dieudonnè determinant does not lie in A. |
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