Regular bi-interpretability of Chevalley groups over local rings

Research output: Contribution to journalArticlepeer-review


We prove that if G(R) = Gπ(Φ , R) (E(R) = Eπ(Φ , R)) is an (elementary) Chevalley group of rank > 1 , R is a local ring (with 12 for the root systems A2, Bl, Cl, F4, G2 and with 13 for G2) , then the group G(R) (or (E(R)) is regularly bi-interpretable with the ring R. As a consequence of this theorem, we show that the class of all Chevalley groups over local rings (with the listed restrictions) is elementarily definable, i.e., if for an arbitrary group H we have H≡ Gπ(Φ , R) , then there exists a ring R≡ R such that H≅ Gπ(Φ , R) .

Original languageEnglish
Article number64
JournalEuropean Journal of Mathematics
Issue number3
StatePublished - Sep 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.


  • Chevalley groups
  • Elementary definability
  • Local rings
  • Regular bi-interpretability


Dive into the research topics of 'Regular bi-interpretability of Chevalley groups over local rings'. Together they form a unique fingerprint.

Cite this