Quadratic modules in 𝑅[[𝑋]]

Augustin, Doris; Knebusch, Manfred

doi:10.1090/S0002-9939-09-10043-6

Quadratic modules in $R[[X]]$
HTML articles powered by AMS MathViewer

by Doris Augustin and Manfred Knebusch PDF

Proc. Amer. Math. Soc. 138 (2010), 75-84 Request permission

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

D. Augustin, The membership problem for quadratic modules with focus on the one dimensional case, Doctoral Dissertation, Universität Regensburg, 2008.
Jacek Bochnak, Michel Coste, and Marie-Françoise Roy, Real algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 36, Springer-Verlag, Berlin, 1998. Translated from the 1987 French original; Revised by the authors. MR 1659509, DOI 10.1007/978-3-662-03718-8
Manfred Knebusch and Claus Scheiderer, Einführung in die reelle Algebra, Vieweg Studium: Aufbaukurs Mathematik [Vieweg Studies: Mathematics Course], vol. 63, Friedr. Vieweg & Sohn, Braunschweig, 1989 (German). MR 1029278, DOI 10.1007/978-3-322-85033-1
T. Y. Lam, An introduction to real algebra, Rocky Mountain J. Math. 14 (1984), no. 4, 767–814. Ordered fields and real algebraic geometry (Boulder, Colo., 1983). MR 773114, DOI 10.1216/RMJ-1984-14-4-767
Murray Marshall, Positive polynomials and sums of squares, Mathematical Surveys and Monographs, vol. 146, American Mathematical Society, Providence, RI, 2008. MR 2383959, DOI 10.1090/surv/146
Alexander Prestel and Charles N. Delzell, Positive polynomials, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2001. From Hilbert’s 17th problem to real algebra. MR 1829790, DOI 10.1007/978-3-662-04648-7
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.