Acta Mathematica Vietnamica

, Volume 44, Issue 2, pp 553–569 | Cite as

On Weakly Locally Finite Division Rings

  • Trinh Thanh DeoEmail author
  • Mai Hoang Bien
  • Bui Xuan Hai


Weakly locally finite division rings were considered in Deo et al. (J. Algebra 365, 42–49, 2012), where it was mentioned that the class of weakly locally finite division rings properly contains the class of locally finite division rings. In this paper, for any integer n ≥ 0 or n = , we construct a weakly locally finite division ring whose Gelfand-Kirillov dimension is n. This fact shows in particular that there exist infinitely many weakly locally finite division rings that are not locally finite. Further, for the class of weakly locally finite division rings, we investigate some questions related with the well-known Kurosh Problem and with one of Herstein’s conjectures.


Division rings Weakly locally finite Gelfand-Kirrilov dimension Linear groups 

Mathematics Subject Classification (2010)

16K40 16P90 



The authors would like to thank the referee for his/her comments and suggestions. Also, they sincerely thank Adrian Wadsworth and John McConnell for the conversations by e-mail about McConnell’s construction of examples of locally PI, but not PI division rings of arbitrary GK-dimension.

Funding Information

This work is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.04-2016.18.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Trinh Thanh Deo
    • 1
    Email author
  • Mai Hoang Bien
    • 1
  • Bui Xuan Hai
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceVNUHCM - University of ScienceHo Chi Minh CityVietnam

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