ON GROUPS AND RINGS DEFINABLE IN O-MINIMAL EXPANSIONS OF REAL CLOSED FIELDS

Authors
OTERO M PETERZIL Y PILLAY A
Citation
M. Otero et al., ON GROUPS AND RINGS DEFINABLE IN O-MINIMAL EXPANSIONS OF REAL CLOSED FIELDS, Bulletin of the London Mathematical Society, 28, 1996, pp. 7-14
Citations number
10
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Bulletin of the London Mathematical Society → ACNP
ISSN journal
00246093
Volume
28
Year of publication
1996
Part
1
Pages
7 - 14
Database
ISI
SICI code
0024-6093(1996)28:<7:OGARDI>2.0.ZU;2-J
Abstract
Let [R, <, +, .] be a real closed field, and let M be an o-minimal exp ansion of R. We prove here several results regarding rings and groups which are definable in M. We show that every M-definable ring without zero divisors is definably isomorphic to R, R(root/(-1)) or the ring o f quaternions over R. One corollary is that no model of T-exp is inter pretable in a model of T-an.