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

Jean-Camille Birget·Stuart W. Margolis
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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.

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Jean-Camille Birget, Stuart W. Margolis. 2001-12-20. A complete rewrite system and normal forms for (S)_reg. https://arxiv.org/abs/math/0112229

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