Completions of Convexly Ordered Valuation Rings

✍ Scribed by Larry Mathews

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 699 KB
• Volume: 40
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19940400303

✦ Synopsis

Abstract

We prove that every convexly ordered valuation ring has a unique completion as a uniform space, which furthermore is a convexly ordered valuation ring. In addition, we give a model theoretic characterisation of complete convexly ordered valuation rings, and give a necessary and sufficient condition for the completion of a convexly ordered valuation ring to be a real closed ring.

Mathematics Subject Classification: 03C60, 13L05, 54E15.