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Quadratic modules in ![$ R[[X]]$](/proc/2010-138-01/S0002-9939-09-10043-6/gif-title0/img1.gif)
Author(s):
Doris
Augustin;
Manfred
Knebusch
Journal:
Proc. Amer. Math. Soc.
138
(2010),
75-84.
MSC (2000):
Primary 13J05, 13J30;
Secondary 06F25
Posted:
August 20, 2009
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Additional information
Abstract:
We give a complete list of all quadratic modules and inclusions between them in the ring ![$ R[[X]]$](/proc/2010-138-01/S0002-9939-09-10043-6/gif-abstract0/img1.gif) of formal power series in one variable  over a euclidean field  .
References:
-
- [A]
- D. Augustin, The membership problem for quadratic modules with focus on the one dimensional case, Doctoral Dissertation, Universität Regensburg, 2008.
- [BCR]
- J. Bochnak, M. Coste and M.-F. Roy, Real algebraic geometry, Springer, Berlin, 1998. MR 1659509 (2000a:14067)
- [KS]
- M. Knebusch and C. Scheiderer, Einführung in die reelle Algebra, Vieweg, Braunschweig, 1989. MR 1029278 (90m:12005)
- [L]
- T. Y. Lam, An introduction to real algebra, Rocky Mtn. J. Math. 14 (1984) 767-814. MR 773114 (86g:12013)
- [M]
- M. Marshall, Positive polynomials and sums of squares, Math. Surveys and Monographs, 146, Amer. Math. Soc., Providence, RI, 2008. MR 2383959 (2009a:13044)
- [PD]
- A. Prestel and C. N. Delzell, Positive polynomials - from Hilbert's 17th problem to real algebra, Springer-Verlag, Berlin, 2001. MR 1829790 (2002k:13044)
- [S]
- C. Scheiderer, Positivity and sums of squares: A guide to recent results, in: Emerging Applications of Algebraic Geometry (M. Putinar, S. Sullivant, eds.), IMA Volumes Math. Appl., 149, Springer, 2009, pp. 271-324.
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Additional Information:
Doris
Augustin
Affiliation:
Universität Regensburg, NWF I - Mathematik, D-93040 Regensburg, Germany
Email:
doris.augustin@mathematik.uni-regensburg.de
Manfred
Knebusch
Affiliation:
Universität Regensburg, NWF I - Mathematik, D-93040 Regensburg, Germany
Email:
manfred.knebusch@mathematik.uni-regensburg.de
DOI:
10.1090/S0002-9939-09-10043-6
PII:
S 0002-9939(09)10043-6
Keywords:
Quadratic modules,
preorderings,
formal power series rings
Received by editor(s):
July 15, 2008,
Received by editor(s) in revised form:
May 5, 2009
Posted:
August 20, 2009
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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