Groups and rings definable in d-minimal structures

2012/05/18 by Antongiulio Fornasiero, Fornasiero, Antongiulio · 2 citations
Mathematics · #03C64 (Primary) 12J15 #22E15 (Secondary) #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1205.4177

openalex publication_date 2012/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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