Submission date: 18 May 2012.

Abstract:

We study groups and rings definable in d-minimal expansions of ordered fields. We generalize to such objects some known results from o-minimality. In particular, we prove that we can endow a definable group with a definable topology making it a topological group, and that a definable ring of dimension at least 1 and without zero divisors is a skew field.

Mathematics Subject Classification: 03C64 (Primary) 12J15, 22E15 (Secondary)

Keywords and phrases:

Full text arXiv 1205.4177: pdf, ps.