Sums of squares in real rings

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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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Official URL: http://www.ams.org/journals/tran/2004-356-07/S0002-9947-03-03438-X/S0002-9947-03-03438-X.pdf




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
Deposited On:10 May 2012 08:42
Last Modified:08 Aug 2018 11:30

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