A Proof of the Conjecture by Carpentier-De Sole-Kac
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🧮 math.RA
keywords
differentialconjecturecarpentiercarpentier-decoefficentsdegeneracydegreedeterminant
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We prove the following conjecture by S. Carpentier, A. De Sole, and V. G. Kac: Let K be a differential field and R be a differential subring of K. Let M be a matrix whose elements are differential operators with coefficents in R. Then, if M has degeneracy degree 1, the Dieudonne' determinant of M lies in R.
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