Tressl, Marcus (2008) Bounded super real closed rings. [MIMS Preprint]
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Abstract
This note is a complement to the paper "M. Tressl, Super real closed rings", where super real closed rings are introduced and studied. A bounded super real closed ring A is a commutative unital ring A together with an operation FA:An -> A for every bounded continuous map F:ℝn -> ℝ, so that all term equalities between the F's remain valid for the FA's. We show that bounded super real closed rings are precisely the convex subrings of super real closed rings: for every bounded super real closed ring there is a largest super real closed subring B contained in A and a smallest super real closed ring C containing A. Moreover B is convex in C. The assignment A↦C is an idempotent mono-reflector from bounded to arbitrary super real closed rings which allows to transfer many of the algebraic results from the unbounded to the bounded situation
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | real closed rings, rings of continuous functions, model theory |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations MSC 2010, the AMS's Mathematics Subject Classification > 46 Functional analysis |
| Depositing User: | Dr Marcus Tressl |
| Date Deposited: | 10 Oct 2008 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1156 |
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