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Title: Axioms for trimedial quasigroups (English)
Author: Kinyon, Michael K.
Author: Phillips, J. D.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 45
Issue: 2
Year: 2004
Pages: 287-294
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Category: math
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Summary: We give new equations that axiomatize the variety of trimedial quasigroups. We also improve a standard characterization by showing that right semimedial, left F-quasigroups are trimedial. (English)
Keyword: trimedial quasigroup
Keyword: F-quasigroup
Keyword: semimedial quasigroup
MSC: 20A05
MSC: 20N05
idZBL: Zbl 1101.20040
idMR: MR2075277
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Date available: 2009-05-05T16:45:13Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/119458
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Reference: [1] Belousov V.D.: Foundations of the Theory of Quasigroups and Loops.Izdat. Nauka, Moscow, 1967 (Russian); MR 36{#}1569, Zbl 163:01801. MR 0218483
Reference: [2] Belousov V.D.: About one quasigroup class (Russian).Uchenye zapiski Beltskogo gospedinstituta im. A. Russo 5 (1960), 29-44.
Reference: [3] Belousov V.D.: Elements of Quasigroup Theory: A Special Course (in Russian).Kishinev State University Press, Kishinev, 1981.
Reference: [4] Bruck R.H.: Some results in the theory of quasigroups.Trans. Amer. Math. Soc. 55 (1944), 19-52; MR 5,229d, Zbl 0063.00635. Zbl 0063.00635, MR 0009963
Reference: [5] Bruck R.H.: A Survey of Binary Systems.Springer-Verlag, 1971; MR 20{#}76, Zbl 206:30301. Zbl 0141.01401, MR 0093552
Reference: [6] Chein O., Pflugfelder H.O., Smith J.D.H. (eds.): Quasigroups and Loops: Theory and Applications.Sigma Series in Pure Math. 9, Heldermann Verlag, 1990; MR 93g:21033, Zbl 0719.20036. Zbl 0719.20036, MR 1125806
Reference: [7] Kepka T.: Structure of triabelian quasigroups.Comment. Math. Univ. Carolinae 17 (1976), 229-240; MR 53{#}10965, Zbl 0338.20097. Zbl 0338.20097, MR 0407182
Reference: [8] Kepka T.: A note on WA-quasigroups.Acta Univ. Carolin. Math. Phys. 19 (1978), 2 61-62; MR 80b:20094, Zbl 0382.20057. Zbl 0382.20057, MR 0509348
Reference: [9] Kepka T.: F-quasigroups isotopic to Moufang loops.Czechoslovak Math. J. 29 (1979), 62-83; MR 80b:20095, Zbl 0444.20067. Zbl 0444.20067, MR 0518141
Reference: [10] Kepka T., Kinyon M.K., Phillips: The structure of F-quasigroups.in preparation. Zbl 1133.20051
Reference: [11] Kinyon M.K., Phillips J.D.: A note on trimedial quasigroups.Quasigroups & Related Systems 9 (2002), 65-66; CMP 1 943 753, Zbl pre01894750. Zbl 1023.20034
Reference: [12] McCune W.W.: OTTER $3.3$ Reference Manual and Guide.Technical Memorandum ANL/MCS-TM-263, Argonne National Laboratory, 2003; or see http://www.mcs.anl.gov/AR/otter/.
Reference: [13] Murdoch D.C.: Quasi-groups which satisfy certain generalized associative laws.Amer. J. Math. 61 (1939), 509-522; Zbl 0020.34702. Zbl 0020.34702, MR 1507391
Reference: [14] Pflugfelder H.O.: Quasigroups and Loops: Introduction.Sigma Series in Pure Math. 8, Heldermann Verlag, Berlin, 1990; MR 93g:20132, Zbl 719:20036. Zbl 0715.20043, MR 1125767
Reference: [15] Toyoda K.: On axioms of linear functions.Proc. Imp. Acad. Tokyo 17 (1941), 221-227; MR 7,241g, Zbl 0061.02403. Zbl 0061.02403, MR 0014105
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