Hilbert series of T-spaces

A. Ya Belov, L. Centrone, S. Malev

Research output: Contribution to journalArticlepeer-review


We show that the Hilbert series of a T-space in a free associative algebra A is either a rational function, or differs from the Hilbert series of the commutator [A,A] by a rational function.

Original languageEnglish
Pages (from-to)350-361
Number of pages12
JournalJournal of Algebra
StatePublished - 15 Aug 2023

Bibliographical note

Funding Information:
This work was supported by Israel Science Foundation , grant No 1994/20 .

Funding Information:
We are grateful to Professor A.V. Mikhalev, who past away 27-th of October of 2022, for useful discussions and to the referee for his/her remarks and suggestions. This work was supported by Israel Science Foundation, grant No 1994/20. The authors are also deeply grateful to the referee: her/his suggestions improved significantly the exposition of the paper. The second author wants to thank GNSAGA of Istituto Nazionale di Alta Matematica (INDAM).

Publisher Copyright:
© 2023 Elsevier Inc.


  • Hilbert series
  • PI-algebra
  • Regular word
  • T-space


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