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Locally modular geometries in homogeneous structures
Author(s) -
Hyttinen Tapani
Publication year - 2005
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200410031
Subject(s) - modular design , mathematics , homogeneous , countable set , affine transformation , division (mathematics) , pure mathematics , ring (chemistry) , type (biology) , division ring , similarity (geometry) , discrete mathematics , combinatorics , arithmetic , image (mathematics) , computer science , artificial intelligence , programming language , ecology , biology , chemistry , organic chemistry
We show that if M is a strongly minimal large homogeneous structure in a countable similarity type and the pregeometry of M is locally modular but not modular, then the pregeometry is affine over a division ring. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)