A complete rewrite system and normal forms for (S)_reg
Group Theory
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0112229,
title = {A complete rewrite system and normal forms for (S)_reg},
author = {Jean-Camille Birget and Stuart W. Margolis},
journal= {arXiv preprint arXiv:math/0112229},
year = {2007}
}