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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Structural monoids associated to equational varieties
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by Patrick Dehornoy PDF
Proc. Amer. Math. Soc. 117 (1993), 293-304 Request permission

Abstract:

Monoids of elementary transformations are associated to certain equational varieties in order to describe the corresponding free objects; in some regular cases, these monoids reduce to groups, and the word problem for the free objects of the variety is connected with the existence of normal forms for the members of the associated group.
References
  • Ronald V. Book, Thue systems as rewriting systems, J. Symbolic Comput. 3 (1987), no. 1-2, 39–68. Rewriting techniques and applications (Dijon, 1985). MR 893185, DOI 10.1016/S0747-7171(87)80021-4
  • E. Brieskorn, Automorphic sets and braids and singularities, Braids (Santa Cruz, CA, 1986) Contemp. Math., vol. 78, Amer. Math. Soc., Providence, RI, 1988, pp. 45–115. MR 975077, DOI 10.1090/conm/078/975077
  • P. Cartier, Développements récents sur les groupes de tresses, applications à la topologie et à l’algèbre, Séminaire Bourbaki, exposé 716, 1989.
  • P. M. Cohn, Universal algebra, Harper & Row, Publishers, New York-London, 1965. MR 0175948
  • Patrick Dehornoy, Free distributive groupoids, J. Pure Appl. Algebra 61 (1989), no. 2, 123–146. MR 1025918, DOI 10.1016/0022-4049(89)90009-1
  • Patrick Dehornoy, Sur la structure des gerbes libres, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), no. 3, 143–148 (French, with English summary). MR 1005627
  • —, Problème de mots dans les gerbes libres, Proc. des Journées Mathématiques-Informatique (Marseille 1989), Theoretical Computer Science (to appear). —, An alternative proof of Laver’s results on the algebra generated by elementary embeddings, preprint, 1989. R. Fenn and C. Rourke, Preliminary announcement of results: racks, links and $3$-manifolds preprint, 1990. G. Huet and D. Oppen, Equations and rewrite rules, Formal Language Theory: Perspectives and Open Problems (R. Book, ed.), Academic Press, New York, 1980, pp. 349-405.
  • David Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982), no. 1, 37–65. MR 638121, DOI 10.1016/0022-4049(82)90077-9
  • Richard Laver, The left distributive law and the freeness of an algebra of elementary embeddings, Adv. Math. 91 (1992), no. 2, 209–231. MR 1149623, DOI 10.1016/0001-8708(92)90016-E
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 117 (1993), 293-304
  • MSC: Primary 08B20; Secondary 20F05, 20M07
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1107919-3
  • MathSciNet review: 1107919