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Algebraic properties of the shift mapping


Author: Patrick Dehornoy
Journal: Proc. Amer. Math. Soc. 106 (1989), 617-623
MSC: Primary 17A30; Secondary 03E55, 17A50
DOI: https://doi.org/10.1090/S0002-9939-1989-0969519-4
MathSciNet review: 969519
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Abstract: We investigate the algebraic structure generated by the "shift" mapping $ n \to n + 1$ on $ {\mathbf{N}}$ under composition and another operation defined below. This allows to prove results about certain free autodistributive structures.


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

  • [1] Patrick Dehornoy, Infinite products in monoids, Semigroup Forum 34 (1986), 21-68. MR 863838 (88b:20107)
  • [2] -, $ {\Pi _1}$-complete families of elementary sequences, Ann. Pure Appl. Logic 38 (1988), 257-287. MR 942526 (89i:03071)
  • [3] -, Free distributive groupoids, J. Pure Appl. Algebra (to appear). MR 1025918 (90j:20135)
  • [4] Randall Dougherty, A note on critical points of elementary embeddings, Notes.
  • [5] Jozef Dudek, Some remarks on distributive groupoids, Czechoslovak Math. J. 31, 106 (1981), 451-456. MR 626918 (82k:20095)
  • [6] David Joyce, A classifying invariant of the knot, the knot quandle, J. Pure Appl. Algebra 23 (1982), 37-66. MR 638121 (83m:57007)
  • [7] -, Simple quandles, J. Algebra 79 (1982), 307-318. MR 682881 (84d:20078)
  • [8] Tomas Kepka, Notes on left-distributive groupoids, Acta Univ. Carolin.-Math. Phys. 22 (1981), 23-37. MR 654379 (83f:20070)
  • [9] Nabuo Nobusawa, A remark on conjugacy classes in simple groups, Osaka J. Math. 18 (1981), 749-754. MR 635731 (82k:20056)
  • [10] R. S. Pierce, Symmetric groupoids, Osaka J. Math. 15 (1978), 51-76 & 16 (1979), 317-348. MR 0480780 (58:930)
  • [11] Sherman Stein, Left distributive quasigroups, Proc. Amer. Math. Soc. 10 (1959), 577-578. MR 0108547 (21:7263)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0969519-4
Article copyright: © Copyright 1989 American Mathematical Society

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