TY - JOUR
T1 - A Complete Rewrite System and Normal Forms for (S)reg
AU - Birget, Jean Camille
AU - Margolis, Stuart W.
PY - 2002/11
Y1 - 2002/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0041920792&partnerID=8YFLogxK
U2 - 10.1007/s002330010138
DO - 10.1007/s002330010138
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AN - SCOPUS:0041920792
SN - 0037-1912
VL - 65
SP - 348
EP - 373
JO - Semigroup Forum
JF - Semigroup Forum
IS - 3
ER -