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Almost associative operations generating a minimal clone

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EN
Abstrakty
EN
Characterizations of 'almost associative' binary operations generating a minimal clone are given for two interpretations of the term 'almost associative'. One of them uses the associative spectrum, the other one uses the index of nonassociativity to measure how far an operation is from being associative.
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Twórcy
  • Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H6720, Szeged, Hungary
Bibliografia
  • [1] V.G. Bodnarčuk, L.A. Kalužnin, V.N. Kotov and B.A. Romov, Galois theory for Post algebras I-II, Kibernetika (Kiev) 3 (1969), 1-10; 5 (1969), 1-9 (Russian).
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  • [4] B. Csákány, All minimal clones on the three-element set, Acta Cybernet. 6 (3) (1983), 227-238.
  • [5] B. Csákány, On conservative minimal operations, Lectures in Universal Algebra (Szeged, 1983), Colloq. Math. Soc. János Bolyai, North-Holland, Amsterdam, 43 (1986), 49-60.
  • [6] B. Csákány and T. Waldhauser, Associative spectra of binary operations, Mult.-Valued Log. 5 (3) (2000), 175-200.
  • [7] A. Drápal and T. Kepka, Sets of associative triples, Europ. J. Combinatorics 6 (1985), 227-231.
  • [8] D. Geiger, Closed systems and functions of predicates, Pacific J. Math. 27 (1968), 95-100.
  • [9] P. Hájek, Die Szászschen Gruppoide, Mat.-Fys. Časopis Sloven. Akad. Vied 15 (1) (1965), 15-42 (German).
  • [10] P. Hájek, Berichtigung zu meiner arbeit 'Die Szászschen Gruppoide', Mat.-Fys. Časopis Sloven. Akad. Vied 15 (4) (1965) 331 (German).
  • [11] J. Ježek and R.W. Quackenbush, Minimal clones of conservative functions, Internat. J. Algebra Comput. 5 (6) (1995), 615-630.
  • [12] K.A. Kearnes, Minimal clones with abelian representations, Acta Sci. Math. (Szeged) 61 (1-4) (1995), 59-76.
  • [13] K.A. Kearnes and Á. Szendrei, The classification of commutative minimal clones, Discuss. Math. Algebra and Stochastic Methods 19 (1) (1999), 147-178.
  • [14] T. Kepka and M. Trch, Groupoids and the associative law I. (Associative triples), Acta Univ. Carol. Math. Phys. 33 (1) (1992), 69-86.
  • [15] T. Kepka and M. Trch, Groupoids and the associative law II. (Groupoids with small semigroup distance), Acta Univ. Carol. Math. Phys. 34 (1) (1993), 67-83.
  • [16] T. Kepka and M. Trch, Groupoids and the associative law III. (Szász-Hájek groupoids), Acta Univ. Carol. Math. Phys. 36 (1) (1995), 17-30.
  • [17] T. Kepka and M. Trch, Groupoids and the associative law IV. (Szász-Hájek groupoids of type (a,b,a)), Acta Univ. Carol. Math. Phys. 35 (1) (1994), 31-42.
  • [18] T. Kepka and M. Trch, Groupoids and the associative law V. (Szász-Hájek groupoids of type (a,a,b)), Acta Univ. Carol. Math. Phys. 36 (1) (1995), 31-44.
  • [19] T. Kepka and M. Trch, Groupoids and the associative law VI. (Szász-Hájek groupoids of type (a,b,c)), Acta Univ. Carol. Math. Phys. 38 (1) (1997), 13-22.
  • [20] L. Lévai and P.P. Pálfy, On binary minimal clones, Acta Cybernet. 12 (3) (1996), 279-294.
  • [21] P.P. Pálfy, Minimal clones, Preprint of the Math. Inst. Hungarian Acad. Sci. 27/1984.
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  • [24] E. Post, The two-valued iterative systems of mathematical logic, Annals of Mathematics Studies, No. 5, Princeton University Press, Princeton 1941.
  • [25] I.G. Rosenberg, Minimal clones I. The five types, Lectures in Universal Algebra (Szeged, 1983), Colloq. Math. Soc. János Bolyai, North-Holland, Amsterdam, 43 (1986), 405-427.
  • [26] N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences, http://www.research.att.com/~njas/sequences, 2005.
  • [27] G. Szász, Die Unabhängigkeit der Assoziativitätsbedingungen, Acta Sci. Math. (Szeged) 15 (1953), 20-28 (German).
  • [28] B. Szczepara, Minimal clones generated by groupoids, Ph.D. Thesis, Université de Montréal 1995.
  • [29] Á. Szendrei, Clones in Universal Algebra, Séminaire de Mathématiques Supérieures, 99, Presses de L'Université de Montréal 1986.
  • [30] M.B. Szendrei, On closed sets of term functions on bands, Semigroups (Proc. Conf., Math. Res. Inst., Oberwolfach, 1978), pp. 156-181, Lecture Notes in Math., 855, Springer, Berlin 1981.
  • [31] T. Waldhauser, Minimal clones generated by majority operations, Algebra Universalis 44 (1,2) (2000), 15-26.
  • [32] T. Waldhauser, Minimal clones with weakly abelian representations, Acta Sci. Math. (Szeged) 69 (3,4) (2003), 505-521.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1104
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