# zbMATH — the first resource for mathematics

On expressing commutativity by finite Church-Rosser presentations: A note on commutative monoids. (English) Zbl 0542.20038
Let T be a finite Church-Rosser Thue System on a finite alphabet $$\Sigma$$ and denote by M the monoid presented by T. Suppose that M is commutative. Then it is shown that if M is cancellative or T is a special Thue system then M is either the free cyclic group or the free cyclic monoid.
Reviewer: D.B.McAlister

##### MSC:
 20M10 General structure theory for semigroups 20M14 Commutative semigroups
Full Text:
##### References:
 [1] 1. A. M. BALLANTYNE and D. S. LANKFORD, New Decision Algorithms for Finitely Presented Commutative Semigroups, Computation and Mathematics with Applications, Vol. 7, 1981, pp. 159-165. Zbl0449.20059 MR619758 · Zbl 0449.20059 · doi:10.1016/0898-1221(81)90115-2 [2] 2. R. BOOK, Decidable Sentences of Church-Rosser Congruences, Theoret. Comput. Sc., Vol. 24, 1983, pp. 301-312. Zbl0525.68015 MR716826 · Zbl 0525.68015 · doi:10.1016/0304-3975(83)90005-1 [3] 3. Y. COCHET, Church-Rosser Congruences on Free Semigroups, Colloquia Math. Soc. Janos Bolyai, Vol. 20, 1976, pp. 51-60. Zbl0408.20054 MR541109 · Zbl 0408.20054 [4] 4. Y. COCHET and M. NIVAT, Une generalisation des ensembles de Dyck, Israël J. Math., Vol. 9, 1971, pp. 389-395. Zbl0215.56005 MR276021 · Zbl 0215.56005 · doi:10.1007/BF02771689 [5] 5. S. EILENBERG and M. P. SCHUTZENBERGER, Rational Sets in Commutative Monoids, J. Algebra, Vol. 13, 1969, pp. 173-191. Zbl0206.02703 MR246985 · Zbl 0206.02703 · doi:10.1016/0021-8693(69)90070-2 [6] 6. G. HUET, Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems, J. Assoc. Comput. Mach., Vol. 27, 1980, pp. 797-821. Zbl0458.68007 MR594700 · Zbl 0458.68007 · doi:10.1145/322217.322230 [7] 7. C. Ó’DÚNLAING, Finite and Infinite Regular Thue Systems, Ph. D. dissertation, University of California at Santa Barbara, 1981. [8] 8. L. REDEI, The Theory of Finitely Generated Commutative Semigroups, Pergamon Press, 1965. Zbl0133.27904 MR188322 · Zbl 0133.27904 [9] 9. J. SAKAROVITCH, Sur les monoides commutatifs, Séminaire d’Informatique Theorique, Institut de Programmation, n^\circ 1, 1978, pp. 78-01.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.