Hilbert's 17th Problem for Real Closed Rings

✍ Scribed by Larry Mathews

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 594 KB
• Volume: 40
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19940400403

✦ Synopsis

Abstract

We recall the characterisation of positive definite polynomial functions over a real closed ring due to Dickmann, and give a new proof of this result, based upon ideas of Abraham Robinson. In addition we isolate the class of convexly ordered valuation rings for which this characterisation holds.

Mathematics Subject Classification: 03C60, 13L05, 12D15.