On the ring of constants for derivations of power series rings in two variables

Leonid Makar-Limanov; Andrzej Nowicki

On the ring of constants for derivations of power series rings in two variables

Leonid Makar-Limanov; Andrzej Nowicki

Colloquium Mathematicae (2001)

Volume: 87, Issue: 2, page 195-200
ISSN: 0010-1354

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Abstract

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Let k[[x,y]] be the formal power series ring in two variables over a field k of characteristic zero and let d be a nonzero derivation of k[[x,y]]. We prove that if Ker(d) ≠ k then Ker(d) = Ker(δ), where δ is a jacobian derivation of k[[x,y]]. Moreover, Ker(d) is of the form k[[h]] for some h ∈ k[[x,y]].

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Leonid Makar-Limanov, and Andrzej Nowicki. "On the ring of constants for derivations of power series rings in two variables." Colloquium Mathematicae 87.2 (2001): 195-200. <http://eudml.org/doc/284176>.

@article{LeonidMakar2001,
abstract = {Let k[[x,y]] be the formal power series ring in two variables over a field k of characteristic zero and let d be a nonzero derivation of k[[x,y]]. We prove that if Ker(d) ≠ k then Ker(d) = Ker(δ), where δ is a jacobian derivation of k[[x,y]]. Moreover, Ker(d) is of the form k[[h]] for some h ∈ k[[x,y]].},
author = {Leonid Makar-Limanov, Andrzej Nowicki},
journal = {Colloquium Mathematicae},
keywords = {Jacobian derivation; formal power series ring},
language = {eng},
number = {2},
pages = {195-200},
title = {On the ring of constants for derivations of power series rings in two variables},
url = {http://eudml.org/doc/284176},
volume = {87},
year = {2001},
}

TY - JOUR
AU - Leonid Makar-Limanov
AU - Andrzej Nowicki
TI - On the ring of constants for derivations of power series rings in two variables
JO - Colloquium Mathematicae
PY - 2001
VL - 87
IS - 2
SP - 195
EP - 200
AB - Let k[[x,y]] be the formal power series ring in two variables over a field k of characteristic zero and let d be a nonzero derivation of k[[x,y]]. We prove that if Ker(d) ≠ k then Ker(d) = Ker(δ), where δ is a jacobian derivation of k[[x,y]]. Moreover, Ker(d) is of the form k[[h]] for some h ∈ k[[x,y]].
LA - eng
KW - Jacobian derivation; formal power series ring
UR - http://eudml.org/doc/284176
ER -

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