Algebraic properties of the shift mapping
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- by Patrick Dehornoy PDF
- Proc. Amer. Math. Soc. 106 (1989), 617-623 Request permission
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
- Patrick Dehornoy, Infinite products in monoids, Semigroup Forum 34 (1986), no. 1, 21–68. MR 863838, DOI 10.1007/BF02573152
- 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 Randall Dougherty, A note on critical points of elementary embeddings, Notes.
- Józef Dudek, Some remarks on distributive groupoids, Czechoslovak Math. J. 31(106) (1981), no. 3, 451–456. With a loose Russian summary. MR 626918
- 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
- David Joyce, Simple quandles, J. Algebra 79 (1982), no. 2, 307–318. MR 682881, DOI 10.1016/0021-8693(82)90305-2
- 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
- Nobuo Nobusawa, A remark on conjugacy classes in simple groups, Osaka Math. J. 18 (1981), no. 3, 749–754. MR 635731
- R. S. Pierce, Symmetric groupoids, Osaka Math. J. 15 (1978), no. 1, 51–76. MR 480780
- Sherman K. Stein, Left-distributive quasi-groups, Proc. Amer. Math. Soc. 10 (1959), 577–578. MR 108547, DOI 10.1090/S0002-9939-1959-0108547-9
Additional Information
- © Copyright 1989 American Mathematical Society
- 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