A Note on Elementary Derivations

Khoury, 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 -