A generalization of Strassen's Positivstellensatz. Issue 2 (29th August 2020)

• Record Type: Journal Article
• Authors: Fritz, Tobias
• Is Part Of: Communications in algebra. Volume 49:Issue 2(2021)
• Page Start: 482
• Page End: 499
• Publication Date: 2020-08-29
• Subjects: Ordered rings -- ordered semirings -- Positivstellensatz -- real spectrum -- semifield; Primary: 06F25 -- 16Y60 -- Secondary: 12J15 -- 14P10; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1803344
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Strassen's Positivstellensatz is a powerful but little known theorem on preordered commutative semirings satisfying a boundedness condition similar to Archimedeanicity. It characterizes the relaxed preorder induced by all monotone homomorphisms to R + in terms of a condition involving large powers. Here, we generalize and strengthen Strassen's result. As a generalization, we replace the boundedness condition by a polynomial growth condition; as a strengthening, we prove two further equivalent characterizations of the homomorphism-induced preorder in our generalized setting.