The kappa-word problem over DRH

TL;DR

This paper proves the decidability of the kappa-word problem over the pseudovariety DRH, extending previous results from H to a broader class of semigroups and providing a canonical form for elements.

Contribution

It extends the decidability of the kappa-word problem from H to DRH and introduces a canonical form for elements over DRH based on known forms over H.

Findings

Decidability of the kappa-word problem over DRH established.

Canonical form for elements in the free kappa-semigroup over DRH provided.

Extension of Almeida and Zeitoun's work on R-trivial semigroups.

Abstract

Let H be a pseudovariety of groups in which the kappa-word problem is decidable. Here, kappa denotes the canonical implicit signature, which consists of the multiplication and the (omega-1)-power. We prove that the kappa-word problem is also decidable over DRH, the pseudovariety of all finite semigroups whose regular R-classes lie in H. Further, we present a canonical form for elements in the free kappa-semigroup over DRH, based on the knowledge of a canonical form for elements in the free kappa-semigroup over H. This extends work of Almeida and Zeitoun on the pseudovariety of all finite R-trivial semigroups.