On the rings of formal solutions of polynomial differential equations

Maria-Angeles Zurro

Banach Center Publications (1998)

  • Volume: 44, Issue: 1, page 277-292
  • ISSN: 0137-6934

Abstract

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The paper establishes the basic algebraic theory for the Gevrey rings. We prove the Hensel lemma, the Artin approximation theorem and the Weierstrass-Hironaka division theorem for them. We introduce a family of norms and we look at them as a family of analytic functions defined on some semialgebraic sets. This allows us to study the analytic and algebraic properties of this rings.

How to cite

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Zurro, Maria-Angeles. "On the rings of formal solutions of polynomial differential equations." Banach Center Publications 44.1 (1998): 277-292. <http://eudml.org/doc/208891>.

@article{Zurro1998,
abstract = {The paper establishes the basic algebraic theory for the Gevrey rings. We prove the Hensel lemma, the Artin approximation theorem and the Weierstrass-Hironaka division theorem for them. We introduce a family of norms and we look at them as a family of analytic functions defined on some semialgebraic sets. This allows us to study the analytic and algebraic properties of this rings.},
author = {Zurro, Maria-Angeles},
journal = {Banach Center Publications},
keywords = {Gevrey rings; Hensel lemma; Artin approximation theorem; Weierstrass-Hironaka division theorem; semialgebraic sets},
language = {eng},
number = {1},
pages = {277-292},
title = {On the rings of formal solutions of polynomial differential equations},
url = {http://eudml.org/doc/208891},
volume = {44},
year = {1998},
}

TY - JOUR
AU - Zurro, Maria-Angeles
TI - On the rings of formal solutions of polynomial differential equations
JO - Banach Center Publications
PY - 1998
VL - 44
IS - 1
SP - 277
EP - 292
AB - The paper establishes the basic algebraic theory for the Gevrey rings. We prove the Hensel lemma, the Artin approximation theorem and the Weierstrass-Hironaka division theorem for them. We introduce a family of norms and we look at them as a family of analytic functions defined on some semialgebraic sets. This allows us to study the analytic and algebraic properties of this rings.
LA - eng
KW - Gevrey rings; Hensel lemma; Artin approximation theorem; Weierstrass-Hironaka division theorem; semialgebraic sets
UR - http://eudml.org/doc/208891
ER -

References

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  15. [O] S. Ouchi Formal solutions with Gevrey type estimates of nonlinear partial differential equations J. Math. Sci. Univ. Tokyo 1 (1994), 205-237 
  16. [R] C. Rotthaus On the approximation theory of excellent rings Invent. Math. 88 (1987), 39-63 
  17. [T] J. Cl. Tougeron Sur les ensembles semi-analytiques avec conditions Gevrey au bord Ann. Sci. École Norm. Sup. (4) 27 (1994), 173-208 
  18. [Z1] M. A. Zurro Le théorème de division pour les séries Gevrey à plusieurs variables Preprint, University of Valladolid, Spain, 1992 
  19. [Z2] M. A. Zurro The Abhyankar Jung theorem revisited J. Pure Appl. Algebra 90 (1993), 257-282 
  20. [Z3] M. A. Zurro Series y funciones Gevrey en varias variables Ph.D. Thesis, University of Valladolid, Spain, 1994 
  21. [Z4] M. A. Zurro Summability 'au plus petit terme' Studia Math. 113 (1995), 197-198 

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