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THE FINITE BASIS PROBLEM FOR FREE TREE MONOIDS

Part of: Model theory Semigroups

Published online by Cambridge University Press:  08 August 2025

YAN FENG LUO Open the ORCID record for YAN FENG LUO [Opens in a new window] ,
ZHEN FENG JIN Open the ORCID record for ZHEN FENG JIN [Opens in a new window]  and
WEN TING ZHANG Open the ORCID record for WEN TING ZHANG [Opens in a new window]
YAN FENG LUO
Affiliation:
School of Mathematics and Statistics, https://ror.org/01mkqqe32Lanzhou University, Lanzhou, Gansu 730000, PR China e-mail: jinzhf20@lzu.edu.cn
ZHEN FENG JIN
Affiliation:
School of Mathematics and Statistics, https://ror.org/01mkqqe32Lanzhou University, Lanzhou, Gansu 730000, PR China e-mail: luoyf@lzu.edu.cn
WEN TING ZHANG*
Affiliation:
School of Mathematics and Statistics, https://ror.org/01mkqqe32Lanzhou University, Lanzhou, Gansu 730000, PR China
*
e-mail: zhangwt@lzu.edu.cn
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Abstract

For each $n\geq 1$, let $FT_n$ be the free tree monoid of rank n and $E_n$ the full extensive transformation monoid over the finite chain $\{1, 2, \ldots , n\}$. It is shown that the monoids $FT_n$ and $E_{n+1}$ satisfy the same identities. Therefore, $FT_n$ is finitely based if and only if $n\leq 3$.

Keywords

free tree monoidextensive transformation monoidℛ-trivial monoidfinite basis problem

MSC classification

Primary: 20M07: Varieties and pseudovarieties of semigroups
Secondary: 03C05: Equational classes, universal algebra

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 8
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc

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Footnotes

This research was partially supported by the National Natural Science Foundation of China (Grant nos. 12271224, 12171213, 12401017) and the Fundamental Research Funds for the Central University (Grant no. lzujbky-2023-ey06).

References

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