A canonical ordering for free self-distributive systems
HTML articles powered by AMS MathViewer
- by Patrick Dehornoy PDF
- Proc. Amer. Math. Soc. 122 (1994), 31-36 Request permission
Abstract:
We construct in free left distributive systems a natural relation that corresponds to the lexicographical ordering on sequences and proves to be a linear ordering. Applications to a word problem and to a characterization of free objects are given.References
- 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
- Patrick Dehornoy, $\Pi ^1_1$-complete families of elementary sequences, Ann. Pure Appl. Logic 38 (1988), no. 3, 257–287. MR 942526, DOI 10.1016/0168-0072(88)90028-0
- 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
- Patrick Dehornoy, Preuve de la conjecture d’irréflexivité pour les structures distributives libres, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), no. 5, 333–336 (French, with English summary). MR 1153710 R. Dougherty, Critical points of elementary embeddings, preprint, 1989.
- 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
- Louis H. Kauffman, Knots and physics, Series on Knots and Everything, vol. 1, World Scientific Publishing Co., Inc., River Edge, NJ, 1991. MR 1141156, DOI 10.1142/9789812796226
- T. Kepka, Notes on left-distributive groupoids, Acta Univ. Carolin. Math. Phys. 22 (1981), no. 2, 23–37 (English, with Russian and Czech summaries). MR 654379
- 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
- Richard Laver, On the algebra of elementary embeddings of a rank into itself, Adv. Math. 110 (1995), no. 2, 334–346. MR 1317621, DOI 10.1006/aima.1995.1014
- David M. Larue, On braid words and irreflexivity, Algebra Universalis 31 (1994), no. 1, 104–112. MR 1250230, DOI 10.1007/BF01188182
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 31-36
- MSC: Primary 06A05; Secondary 03E55, 08A50, 20N02
- DOI: https://doi.org/10.1090/S0002-9939-1994-1191866-6
- MathSciNet review: 1191866