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Identities and bases in the hypoplactic monoid
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Orientador(es)
Resumo(s)
This paper presents new results on the identities satisfied by the hypoplactic monoid. We show how to embed the hypoplactic monoid of any rank strictly greater than 2 (including infinite rank) into a direct product of copies of the hypoplactic monoid of rank 2. This confirms that all hypoplactic monoids of rank greater than or equal to 2 satisfy exactly the same identities. We then give a complete characterization of those identities, and prove that the variety generated by the hypoplactic monoid has finite axiomatic rank, by giving a finite basis for it.
Descrição
This work is funded by National Funds through the FCT - Fundacao para a Ciencia e a Tecnologia, I.P., under the scope of the project UIDB/00297/2020 (Center for Mathematics and Applications) and the project PTDC/MAT-PUR/31174/2017. The third author is funded by National Funds through the FCT - Fundacao para a Ciencia e a Tecnologia, I.P., under the scope of the studentship SFRH/BD/138949/2018.
Palavras-chave
axiomatic rank equational basis Hypoplactic monoid identities variety Algebra and Number Theory