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

Manfred Kufleitner ^{(1) (2)}, Alexander Lauser ^{(1) (2)}

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

Manfred Kufleitner ^{(1) (2)}, Alexander Lauser ^{(1) (2)}

(1) University of Stuttgart

(2) University of Stuttgart = Universität Stuttgart

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.

Keywords

• [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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