Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Structural monoids associated to equational varieties

Author: Patrick Dehornoy
Journal: Proc. Amer. Math. Soc. 117 (1993), 293-304
MSC: Primary 08B20; Secondary 20F05, 20M07
MathSciNet review: 1107919
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [Bo] R. Book, Thue systems as rewriting systems, J. Symbolic Comput. 3 (1987), 39-68. MR 893185 (88g:03056)
  • [Br] E. Brieskorn, Automorphic sets and braids and singularities, Braids, Contemp. Math., vol. 78, Amer. Math. Soc., Providence, RI, 1988, pp. 45-117. MR 975077 (90a:32024)
  • [Ca] P. Cartier, Développements récents sur les groupes de tresses, applications à la topologie et à l'algèbre, Séminaire Bourbaki, exposé 716, 1989.
  • [Co] P. M. Cohn, Universal algebra, Harper & Row, New York, 1965. MR 0175948 (31:224)
  • [De1] P. Dehornoy, Free distributive groupoids, J. Pure Appl. Algebra 61 (1989), 123-146. MR 1025918 (90j:20135)
  • [De2] -, Sur la structure des gerbes libres, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), 143-148. MR 1005627 (90j:20146)
  • [De3] -, Problème de mots dans les gerbes libres, Proc. des Journées Mathématiques-Informatique (Marseille 1989), Theoretical Computer Science (to appear).
  • [De4] -, An alternative proof of Laver's results on the algebra generated by elementary embeddings, preprint, 1989.
  • [FR] R. Fenn and C. Rourke, Preliminary announcement of results: racks, links and $ 3$-manifolds preprint, 1990.
  • [HO] 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.
  • [Jo] D. Joyce, A classifying invariant of knots: the knot quandle, J. Pure Appl. Algebra 23 (1982), 37-65. MR 638121 (83m:57007)
  • [La] R. Laver, The left distributive law and the freeness of an algebra of elementary embeddings, preprint, 1989. MR 1149623 (93b:08008)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 08B20, 20F05, 20M07

Retrieve articles in all journals with MSC: 08B20, 20F05, 20M07

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society