RT Journal Article T1 Sums of squares in real rings A1 Fernando Galván, José Francisco A1 Ruiz Sancho, Jesús María A1 Scheiderer, Claus AB 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. PB American Mathematical Society SN 0002-9947 YR 2004 FD 2004 LK https://hdl.handle.net/20.500.14352/49910 UL https://hdl.handle.net/20.500.14352/49910 LA eng NO European Research Training Network RAAG NO Spanish Research Project GAAR DS Docta Complutense RD 5 abr 2025