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Sums of squares in real rings

Fernando Galván, José Francisco and Ruiz Sancho, Jesús María and Scheiderer, Claus (2004) Sums of squares in real rings. Transactions of the American Mathematical Society, 356 (7). pp. 2663-2684. ISSN 0002-9947

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Abstract

Let A be an excellent ring. We show that if the real dimension of A is at least three then A has in finite Pythagoras number, and there exists a positive semidefinite element in A which is not a sum of squares in A.

Item Type:Article
Uncontrolled Keywords:Positive semi-definite polynomial; Excellent ring; Real spectrum; Complete local ring
Subjects:Sciences > Mathematics > Number theory
Sciences > Mathematics > Algebraic geometry
ID Code:15168
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