Sections of a~differential spectrum and factorization-free computations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 133-144
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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 $\mathcal R$ without computation of $\operatorname{diffspec}\mathcal R$. 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.
@article{FPM_2003_9_3_a9,
author = {A. I. Ovchinnikov},
title = {Sections of a~differential spectrum and factorization-free computations},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {133--144},
publisher = {mathdoc},
volume = {9},
number = {3},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a9/}
}
A. I. Ovchinnikov. Sections of a~differential spectrum and factorization-free computations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 133-144. http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a9/