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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1104,
author = {Tam\'as Waldhauser},
title = {Almost associative operations generating a minimal clone},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {26},
year = {2006},
pages = {45-73},
zbl = {1102.08002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1104}
}
Tamás Waldhauser. Almost associative operations generating a minimal clone. Discussiones Mathematicae - General Algebra and Applications, Tome 26 (2006) pp. 45-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1104/
[000] [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).
[001] [2] A.C. Climescu, Études sur la théorie des systèmes multiplicatifs uniformes I. L'indice de non-associativité, Bull. École Polytech. Jassy 2 (1947), 347-371 (French).
[002] [3] A.C. Climescu, L'indépendance des conditions d'associativité, Bull. Inst. Polytech. Jassy 1 (1955), 1-9 (Romanian). | Zbl 0068.02901
[003] [4] B. Csákány, All minimal clones on the three-element set, Acta Cybernet. 6 (3) (1983), 227-238. | Zbl 0537.08002
[004] [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.
[005] [6] B. Csákány and T. Waldhauser, Associative spectra of binary operations, Mult.-Valued Log. 5 (3) (2000), 175-200. | Zbl 0999.20054
[006] [7] A. Drápal and T. Kepka, Sets of associative triples, Europ. J. Combinatorics 6 (1985), 227-231. | Zbl 0612.05003
[007] [8] D. Geiger, Closed systems and functions of predicates, Pacific J. Math. 27 (1968), 95-100. | Zbl 0186.02502
[008] [9] P. Hájek, Die Szászschen Gruppoide, Mat.-Fys. Časopis Sloven. Akad. Vied 15 (1) (1965), 15-42 (German).
[009] [10] P. Hájek, Berichtigung zu meiner arbeit 'Die Szászschen Gruppoide', Mat.-Fys. Časopis Sloven. Akad. Vied 15 (4) (1965) 331 (German).
[010] [11] J. Ježek and R.W. Quackenbush, Minimal clones of conservative functions, Internat. J. Algebra Comput. 5 (6) (1995), 615-630. | Zbl 0842.08002
[011] [12] K.A. Kearnes, Minimal clones with abelian representations, Acta Sci. Math. (Szeged) 61 (1-4) (1995), 59-76. | Zbl 0841.08001
[012] [13] K.A. Kearnes and Á. Szendrei, The classification of commutative minimal clones, Discuss. Math. Algebra and Stochastic Methods 19 (1) (1999), 147-178. | Zbl 0937.08003
[013] [14] T. Kepka and M. Trch, Groupoids and the associative law I. (Associative triples), Acta Univ. Carol. Math. Phys. 33 (1) (1992), 69-86. | Zbl 0791.20084
[014] [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. | Zbl 0809.20056
[015] [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. | Zbl 0828.20071
[016] [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. | Zbl 0819.20075
[017] [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. | Zbl 0828.20072
[018] [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. | Zbl 0889.20040
[019] [20] L. Lévai and P.P. Pálfy, On binary minimal clones, Acta Cybernet. 12 (3) (1996), 279-294. | Zbl 0880.08001
[020] [21] P.P. Pálfy, Minimal clones, Preprint of the Math. Inst. Hungarian Acad. Sci. 27/1984.
[021] [22] J. Płonka, On groups in which idempotent reducts form a chain, Colloq. Math. 29 (1974), 87-91. | Zbl 0279.20045
[022] [23] J. Płonka, On k-cyclic groupoids, Math. Japon. 30 (3) (1985), 371-382. | Zbl 0572.08004
[023] [24] E. Post, The two-valued iterative systems of mathematical logic, Annals of Mathematics Studies, No. 5, Princeton University Press, Princeton 1941. | Zbl 0063.06326
[024] [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.
[025] [26] N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences, http://www.research.att.com/~njas/sequences, 2005. | Zbl 1274.11001
[026] [27] G. Szász, Die Unabhängigkeit der Assoziativitätsbedingungen, Acta Sci. Math. (Szeged) 15 (1953), 20-28 (German). | Zbl 0051.25203
[027] [28] B. Szczepara, Minimal clones generated by groupoids, Ph.D. Thesis, Université de Montréal 1995.
[028] [29] Á. Szendrei, Clones in Universal Algebra, Séminaire de Mathématiques Supérieures, 99, Presses de L'Université de Montréal 1986.
[029] [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.
[030] [31] T. Waldhauser, Minimal clones generated by majority operations, Algebra Universalis 44 (1,2) (2000), 15-26. | Zbl 1013.08004
[031] [32] T. Waldhauser, Minimal clones with weakly abelian representations, Acta Sci. Math. (Szeged) 69 (3,4) (2003), 505-521. | Zbl 1046.08001