FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 3, PAGES 133-144

Sections of a differential spectrum and factorization-free computations

A. I. Ovchinnikov

Abstract

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We construct sections of a differential spectrum using only localization and projective limits. For this purpose we introduce a special form of a multiplicative system 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 $R$ without computation of $diffspec\; R$. We compare our construction with Kovacic's structure sheaf and with the results obtained by Keigher. We show how to compute sections of factor-rings of rings of differential polynomials. All computations in this paper are factorization-free.

Location: http://mech.math.msu.su/~fpm/eng/k03/k033/k03310h.htm.
Last modified: January 24, 2005.