On groups and rings definable in o-minimal expansions of real closed fields

Margarita Otero; Ya'acov Peterzil; Anand Pillay

doi:10.1112/blms/28.1.7

On groups and rings definable in o-minimal expansions of real closed fields

Margarita Otero, Ya'acov Peterzil, Anand Pillay

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let 〈R, <, +, ·〉 be a real closed field, and let Script M sign be an o-minimal expansion of R. We prove here several results regarding rings and groups which are definable in Script M sign. We show that every Script M sign-definable ring without zero divisors is definably isomorphic to R, R(√(-1)) or the ring of quaternions over R. One corollary is that no model of T_exp is interpretable in a model of T_an.

Original language	English
Pages (from-to)	7-14
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	28
Issue number	1
DOIs	https://doi.org/10.1112/blms/28.1.7
State	Published - Jan 1996

Bibliographical note

Funding Information:
Received 25 May 1993; revised 12 January 1995. 1991 Mathematics Subject Classification 12L12. First author partially supported by a CICYT PB890379C0202 grant. Bull. London Math. Soc. 28 (1996) 7-14

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1112/blms/28.1.7

Cite this

@article{ec4c0cc60c1d4cec9461887c524c9ceb,

title = "On groups and rings definable in o-minimal expansions of real closed fields",

abstract = "Let 〈R, <, +, ·〉 be a real closed field, and let Script M sign be an o-minimal expansion of R. We prove here several results regarding rings and groups which are definable in Script M sign. We show that every Script M sign-definable ring without zero divisors is definably isomorphic to R, R(√(-1)) or the ring of quaternions over R. One corollary is that no model of Texp is interpretable in a model of Tan.",

author = "Margarita Otero and Ya'acov Peterzil and Anand Pillay",

note = "Funding Information: Received 25 May 1993; revised 12 January 1995. 1991 Mathematics Subject Classification 12L12. First author partially supported by a CICYT PB890379C0202 grant. Bull. London Math. Soc. 28 (1996) 7-14",

year = "1996",

month = jan,

doi = "10.1112/blms/28.1.7",

language = "English",

volume = "28",

pages = "7--14",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley and Sons Ltd",

number = "1",

}

TY - JOUR

T1 - On groups and rings definable in o-minimal expansions of real closed fields

AU - Otero, Margarita

AU - Peterzil, Ya'acov

AU - Pillay, Anand

N1 - Funding Information: Received 25 May 1993; revised 12 January 1995. 1991 Mathematics Subject Classification 12L12. First author partially supported by a CICYT PB890379C0202 grant. Bull. London Math. Soc. 28 (1996) 7-14

PY - 1996/1

Y1 - 1996/1

N2 - Let 〈R, <, +, ·〉 be a real closed field, and let Script M sign be an o-minimal expansion of R. We prove here several results regarding rings and groups which are definable in Script M sign. We show that every Script M sign-definable ring without zero divisors is definably isomorphic to R, R(√(-1)) or the ring of quaternions over R. One corollary is that no model of Texp is interpretable in a model of Tan.

AB - Let 〈R, <, +, ·〉 be a real closed field, and let Script M sign be an o-minimal expansion of R. We prove here several results regarding rings and groups which are definable in Script M sign. We show that every Script M sign-definable ring without zero divisors is definably isomorphic to R, R(√(-1)) or the ring of quaternions over R. One corollary is that no model of Texp is interpretable in a model of Tan.

UR - http://www.scopus.com/inward/record.url?scp=0029684172&partnerID=8YFLogxK

U2 - 10.1112/blms/28.1.7

DO - 10.1112/blms/28.1.7

M3 - Article

AN - SCOPUS:0029684172

SN - 0024-6093

VL - 28

SP - 7

EP - 14

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 1

ER -

On groups and rings definable in o-minimal expansions of real closed fields

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this