The ideal of separants in the ring of differential polynomials
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We obtained the criterion of existence of a quasi-linear polynomial in a differential ideal in the ordinary ring of differential polynomials over a field of characteristic zero. We generalized the “going up” and “going down” theorems onto the case of Ritt algebras. In particular, new finiteness criteria for differential standard bases and estimates that characterize calculation complexity were obtained.
KeywordsStandard Basis Characteristic Zero Derivation Operator Ring Homomorphism Quotient Algebra
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