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## One-element differential standard bases with respect to inverse lexicographical orderings

Journal of Mathematical Sciences. 2009. Vol. 163. No. 5. P. 523-533.

Abstract. We give a simplified proof of the following fact: for all nonnegative integers n and d the monomial ydn forms a differential standфard basis of the ideal [ydn ]. In contrast to Levi’s combinatorial proof, in this proof we use the Gr¨obner bases technique. Under some assumptions we prove the converse result: if an isobaric polynomial f forms a differential standard basis of [f], then f = ydn .