Sums of squares in some integral domains

DOI10.1016/0021-8693(80)90248-3zbMath0433.10010OpenAlexW1973838724MaRDI QIDQ1139070

Bruce Reznick, Man-Duen Choi, Tsit-Yuen Lam, A.F.T.W.Rosenberg

Publication date: 1980

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(80)90248-3

zbMATH Keywords

sums of squaresintegral domains

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Valuations and their generalizations for commutative rings (13A18) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Regular local rings (13H05) Local rings and semilocal rings (13H99) Quadratic forms over local rings and fields (11E08)

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Principal homogeneous spaces under flasque tori; applications, Pfister's theorem for varieties and reduced Witt rings, An elementary proof that the length of \(X_1^4+X_2^4+X_3^4+X_4^4\) is 4., Real zeros for positive semidefinite forms. I, The Grothendieck–Serre conjecture over valuation rings, Sums of squares on hypersurfaces, The many aspects of the Pythagorean triangles, Polynomials in $\mathbb {R}[x,y$ that are sums of squares in $\mathbb {R}(x,y)$], On the level of principal ideal domains, Facial reduction for exact polynomial sum of squares decomposition, Sums of squares of regular functions on real algebraic varieties, Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings, Computing the Length of Sum of Squares and Pythagoras Element in a Global Field, On the bad points of positive semidefinite polynomials

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