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

Manfred Kufleitner (1) , Alexander Lauser (1)

1 University of Stuttgart

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.

Domaines: Mathématique discrète [cs.DM]

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, 2012, Vol. 14 no. 1 (1), pp.141-146. ⟨10.46298/dmtcs.564⟩. ⟨hal-00992870⟩