Groups and rings definable in d-minimal structures

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.

arXiv comment24 pages

Cited by in corpus (2)

• Expansions of real closed fields which introduce no new smooth functions
• Groups definable in two orthogonal sorts