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.
Bibliographical noteFunding Information:
This work was supported by Israel Science Foundation , grant No 1994/20 .
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).
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- Hilbert series
- Regular word