Abstract
Let \(\mathfrak A\) be an alphabet and W be a set of words in the free monoid \({\mathfrak A}^*\). Let S(W) denote the Rees quotient over the ideal of \({\mathfrak A}^*\) consisting of all words that are not subwords of words in W. We call a set of words W finitely based if the monoid S(W) is finitely based. We find a simple algorithm that recognizes finitely based words among words with at most two non-linear variables. We also describe syntactically all hereditary finitely based monoids of the form S(W).
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Acknowledgments
The author thanks Gili Golan for her thoughtful comments and Victor Guba for his suggestion to prove Theorem 6.2 by using the argument of Lyndon and Schupp. The author is also very grateful to the anonymous referee for the helpful comments and suggestions.
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Communicated by Marcel Jackson.
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Sapir, O. The finite basis problem for words with at most two non-linear variables. Semigroup Forum 93, 131–151 (2016). https://doi.org/10.1007/s00233-016-9799-4
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DOI: https://doi.org/10.1007/s00233-016-9799-4