Solving power series equations. II. Change of ground field

Joseph Becker

Annales de l'institut Fourier (1979)

  • Volume: 29, Issue: 2, page 1-23
  • ISSN: 0373-0956

Abstract

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We study the effect of changing the residue field, on the topological properties of local algebra homomorphisms of analytic algebras (quotients of convergent power series rings). Although injectivity is not preserved, openness and closedness in the Krull topology, simple topology, and inductive topology is preserved.

How to cite

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Becker, Joseph. "Solving power series equations. II. Change of ground field." Annales de l'institut Fourier 29.2 (1979): 1-23. <http://eudml.org/doc/74408>.

@article{Becker1979,
abstract = {We study the effect of changing the residue field, on the topological properties of local algebra homomorphisms of analytic algebras (quotients of convergent power series rings). Although injectivity is not preserved, openness and closedness in the Krull topology, simple topology, and inductive topology is preserved.},
author = {Becker, Joseph},
journal = {Annales de l'institut Fourier},
keywords = {power series equations; change of ground field; topological properties; analytic algebra},
language = {eng},
number = {2},
pages = {1-23},
publisher = {Association des Annales de l'Institut Fourier},
title = {Solving power series equations. II. Change of ground field},
url = {http://eudml.org/doc/74408},
volume = {29},
year = {1979},
}

TY - JOUR
AU - Becker, Joseph
TI - Solving power series equations. II. Change of ground field
JO - Annales de l'institut Fourier
PY - 1979
PB - Association des Annales de l'Institut Fourier
VL - 29
IS - 2
SP - 1
EP - 23
AB - We study the effect of changing the residue field, on the topological properties of local algebra homomorphisms of analytic algebras (quotients of convergent power series rings). Although injectivity is not preserved, openness and closedness in the Krull topology, simple topology, and inductive topology is preserved.
LA - eng
KW - power series equations; change of ground field; topological properties; analytic algebra
UR - http://eudml.org/doc/74408
ER -

References

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  2. [2] S. S. ABHYANKAR, and M. VAN DER PUT, Homomorphisms of analytic local rings, Creile's J., 42 (1970), 26-60. Zbl0193.00501MR41 #5353
  3. [3] S. S. ABHYANKAR, and T. T. MOH, A reduction theorem for divergent power series, Creile's J., 241 (1970), 27-33. Zbl0191.04403MR41 #3800
  4. [4] M. ARTIN, Algebraic approximation of structures over complete local rings, Inst. des Hautes études Scientifiques Publ. Math., 36 (1969), 23-58. Zbl0181.48802MR42 #3087
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