Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

The Derksen invariant vs. the Makar-Limanov invariant

Author(s): Anthony Crachiola; Stefan Maubach
Journal: Proc. Amer. Math. Soc. 131 (2003), 3365-3369.
MSC (2000): Primary 14R05; Secondary 13N15
Posted: June 19, 2003
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

Abstract: In this article it is shown that the Makar-Limanov invariant of a ring (or variety) can be trivial while the Derksen invariant is not, and vice versa.

References:

1.
S. Abhyankar, P. Eakin, and W. Heinzer, On the uniqueness of the coefficient ring in a polynomial ring, J. Algebra, 23(1972), 310-342 MR 46:5300

2.
W. Danielewski, On the cancellation problem and automorphism groups of affine algebraic varieties, preprint, Warsaw, (1989)

3.
H. Derksen, Constructive Invariant Theory and the Linearisation Problem, Ph.D. thesis, University of Basel, (1997)

4.
A. van den Essen, Polynomial Automorphisms and the Jacobian Conjecture, in Progress in Math., Vol. 190, Birkhäuser-Verlag, (2000) MR 2001j:14082

5.
L. Makar-Limanov, On the hypersurface $x+x^2y+z^2+t ^3=0$ in $\mathbb{C}^4$ or a $\mathbb{C}^3$-like threefold which is not $\mathbb{C}^3$, Israel J. Math., 96(1996), 419-429 MR 98a:14052

6.
L. Makar-Limanov, Cancellation for curves, preprint

7.
L. Makar-Limanov, Locally nilpotent derivations, a new ring invariant and applications, available at http://www.math.wayne.edu/~lml

8.
L. Makar-Limanov, On the group of automorphisms of a surface $x^n y=P(z)$, Israel J. Math., 121(2001), 113-123 MR 2001m:14086

9.
R. Rentschler, Opérations du groupe additif sur le plan affine, C. R. Acad. Sci. Paris, 267(1968), 384-387 MR 38:1093

10.
A. Seidenberg, Derivations and integral closure, Pacific Journal Math., 16(1966), 167-173 MR 32:5686

11.
W. Vasconcelos, Derivations on commutative noetherian rings, Mathematische Zeitschrift, 112(1969), 229-233 MR 40:7247

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14R05, 13N15

Retrieve articles in all Journals with MSC (2000): 14R05, 13N15

Additional Information:

Anthony Crachiola
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: crach@math.wayne.edu

Stefan Maubach
Affiliation: Department of Mathematics, University of Nijmegen, Toernooiveldt, 6525 ED Nijmegen, The Netherlands
Email: stefanm@sci.kun.nl

DOI: 10.1090/S0002-9939-03-07155-7
PII: S 0002-9939(03)07155-7
Keywords: Makar-Limanov invariant, Derksen invariant, ring invariant, locally nilpotent derivation
Received by editor(s): June 12, 2002
Posted: June 19, 2003
Communicated by: Bernd Ulrich
Copyright of article: Copyright 2003, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google