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Sections of a differential spectrum and factorization-free computations

Abstract

We construct sections of a differential spectrum using only localization and projective limits. For this purpose we introduce a special form of multiplicative systems generated by one differential polynomial and call it D-localization. Owing to this technique one can construct sections of a differential spectrum of a differential ring \(\mathcal{R}\) without computation of diffspec \(\mathcal{R}\). We compare our construction with Kovacic’s structure sheaf and with the results obtained by Keigher [J. Pure Appl. Algebra, 27, 163–172 (1983)]. We show how to compute sections of factor-rings of rings of differential polynomials. All computations in this paper are factorization-free.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 133–144, 2003.

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Ovchinnikov, A.I. Sections of a differential spectrum and factorization-free computations. J Math Sci 135, 3355–3362 (2006). https://doi.org/10.1007/s10958-006-0165-z

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Keywords

  • Special Form
  • Projective Limit
  • Structure Sheaf
  • Differential Spectrum
  • Differential Polynomial