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Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María ; Scheiderer, Claus | American Mathematical Society | 2004Let 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.texto impreso
Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María ; Scheiderer, Claus | International Press | 2006Let k be a real field. We show that every non-negative homogeneous quadratic polynomial f (x(1),..., x(n)) with coefficients in the polynomial ring k[t] is a sum of 2n center dot tau(k) squares of linear forms, where tau(k) is the supremum of th[...]texto impreso
Let A = k[y] be the polynomial ring in one single variable y over a field k. We discuss the number of squares needed to represent sums of squares of linear forms with coefficients in the ring A. We use quaternions to obtain bounds when the Pytha[...]
