On sums of squares in local rings

DOI10.1515/crll.2001.085zbMath0991.13014OpenAlexW2058493131MaRDI QIDQ2754273

Claus Scheiderer

Publication date: 11 November 2001

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/2f68210c4fcc49d86c7593b508724a2c4e243513

zbMATH Keywords

Pythagoras numberreal closed fieldsum of squarespositive semidefinite element

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Local rings and semilocal rings (13H99) Real algebra (13J30)

Related Items (17)

On the Pythagoras numbers of real analytic set germs ⋮ On the Pythagoras numbers of real analytic curves ⋮ Sums of squares in real rings ⋮ Distinguished representations of non-negative polynomials ⋮ Positive semidefinite analytic functions on real analytic surfaces ⋮ A Positivstellensatz for projective real varieties ⋮ Sums of squares on hypersurfaces ⋮ Analytic surface germs with minimal Pythagoras number ⋮ Spectrahedral Shadows ⋮ The Pythagoras number and the \(u\)-invariant of Laurent series fields in several variables ⋮ Sums of squares on real algebraic surfaces ⋮ Sums of squares in real analytic rings ⋮ Weighted sums of squares in local rings and their completions. I ⋮ Weighted sums of squares in local rings and their completions. II ⋮ Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings ⋮ On the bad points of positive semidefinite polynomials ⋮ Positivity, sums of squares and the multi-dimensional moment problem

Cites Work

• On the representation of rational functions as sums of squares
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