A complete rewrite system and normal forms for (S)ᵣeg

Original · EN

The (.)ᵣeg construction was introduced in order to make an arbitrary semigroup S divide a regular semigroup (S)ᵣeg which shares some important properties with S (e.g., finiteness, subgroups, torsion bounds, J-order structure). We show that (S)ᵣeg can be described by a rather simple complete string rewrite system, as a consequence of which we obtain a new proof of the normal form theorem for (S)ᵣeg. The new proof of the normal form theorem is conceptually simpler than the previous proofs.