# A Note on Elementary Derivations

Serdica Mathematical Journal (2004)

- Volume: 30, Issue: 4, page 549-570
- ISSN: 1310-6600

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topKhoury, Joseph. "A Note on Elementary Derivations." Serdica Mathematical Journal 30.4 (2004): 549-570. <http://eudml.org/doc/219656>.

@article{Khoury2004,

abstract = {2000 Mathematics Subject Classification: Primary: 14R10. Secondary: 14R20, 13N15.Let R be a UFD containing a field of characteristic 0, and
Bm = R[Y1, . . . , Ym] be a polynomial ring over R. It was conjectured in [5]
that if D is an R-elementary monomial derivation of B3 such that ker D is
a finitely generated R-algebra then the generators of ker D can be chosen to
be linear in the Yi ’s. In this paper, we prove that this does not hold for B4.
We also investigate R-elementary derivations D of Bm satisfying one or the
other of the following conditions:
(i) D is standard.
(ii) ker D is generated over R by linear constants.
(iii) D is fix-point-free.
(iv) ker D is finitely generated as an R-algebra.
(v) D is surjective.
(vi) The rank of D is strictely less than m.},

author = {Khoury, Joseph},

journal = {Serdica Mathematical Journal},

keywords = {Derivations; Hilbert Fourteenth Problem; polynomial rings; Hilbert fourteenth problem},

language = {eng},

number = {4},

pages = {549-570},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {A Note on Elementary Derivations},

url = {http://eudml.org/doc/219656},

volume = {30},

year = {2004},

}

TY - JOUR

AU - Khoury, Joseph

TI - A Note on Elementary Derivations

JO - Serdica Mathematical Journal

PY - 2004

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 30

IS - 4

SP - 549

EP - 570

AB - 2000 Mathematics Subject Classification: Primary: 14R10. Secondary: 14R20, 13N15.Let R be a UFD containing a field of characteristic 0, and
Bm = R[Y1, . . . , Ym] be a polynomial ring over R. It was conjectured in [5]
that if D is an R-elementary monomial derivation of B3 such that ker D is
a finitely generated R-algebra then the generators of ker D can be chosen to
be linear in the Yi ’s. In this paper, we prove that this does not hold for B4.
We also investigate R-elementary derivations D of Bm satisfying one or the
other of the following conditions:
(i) D is standard.
(ii) ker D is generated over R by linear constants.
(iii) D is fix-point-free.
(iv) ker D is finitely generated as an R-algebra.
(v) D is surjective.
(vi) The rank of D is strictely less than m.

LA - eng

KW - Derivations; Hilbert Fourteenth Problem; polynomial rings; Hilbert fourteenth problem

UR - http://eudml.org/doc/219656

ER -

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