Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
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)

     

Quadratic modules in $ R[[X]]$

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
MathSciNet review: 2550171
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We give a complete list of all quadratic modules and inclusions between them in the ring $ R[[X]]$ of formal power series in one variable $ X$ over a euclidean field $ R$.

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.

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13J05, 13J30, 06F25

Retrieve articles in all Journals with MSC (2000): 13J05, 13J30, 06F25

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.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia