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The Join of the Varieties of R-trivial and L-trivial Monoids via Combinatorics on Words

Abstract : The join of two varieties is the smallest variety containing both. In finite semigroup theory, the varieties of R-trivial and L-trivial monoids are two of the most prominent classes of finite monoids. Their join is known to be decidable due to a result of Almeida and Azevedo. In this paper, we give a new proof for Almeida and Azevedo's effective characterization of the join of R-trivial and L-trivial monoids. This characterization is a single identity of omega-terms using three variables.
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Manfred Kufleitner, Alexander Lauser. The Join of the Varieties of R-trivial and L-trivial Monoids via Combinatorics on Words. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 1 (1), pp.141-146. ⟨hal-00992870⟩

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