Axioms for trimedial quasigroups

Michael K. Kinyon; Jon D. Phillips

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 2, page 287-294
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Kinyon, Michael K., and Phillips, Jon D.. "Axioms for trimedial quasigroups." Commentationes Mathematicae Universitatis Carolinae 45.2 (2004): 287-294. <http://eudml.org/doc/249335>.

@article{Kinyon2004,
abstract = {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.},
author = {Kinyon, Michael K., Phillips, Jon D.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {trimedial quasigroup; F-quasigroup; semimedial quasigroup; trimedial quasigroups; F-quasigroups; semimedial quasigroups; axioms; varieties of quasigroups},
language = {eng},
number = {2},
pages = {287-294},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Axioms for trimedial quasigroups},
url = {http://eudml.org/doc/249335},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Kinyon, Michael K.
AU - Phillips, Jon D.
TI - Axioms for trimedial quasigroups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 2
SP - 287
EP - 294
AB - 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.
LA - eng
KW - trimedial quasigroup; F-quasigroup; semimedial quasigroup; trimedial quasigroups; F-quasigroups; semimedial quasigroups; axioms; varieties of quasigroups
UR - http://eudml.org/doc/249335
ER -

References

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  8. Kepka T., A note on WA-quasigroups, Acta Univ. Carolin. Math. Phys. 19 (1978), 2 61-62; MR 80b:20094, Zbl 0382.20057. (1978) Zbl0382.20057MR0509348
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  10. Kepka T., Kinyon M.K., Phillips, The structure of F-quasigroups, in preparation. Zbl1133.20051
  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. (2002) Zbl1023.20034
  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/. 
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  14. Pflugfelder H.O., Quasigroups and Loops: Introduction, Sigma Series in Pure Math. 8, Heldermann Verlag, Berlin, 1990; MR 93g:20132, Zbl 719:20036. Zbl0715.20043MR1125767
  15. Toyoda K., On axioms of linear functions, Proc. Imp. Acad. Tokyo 17 (1941), 221-227; MR 7,241g, Zbl 0061.02403. (1941) Zbl0061.02403MR0014105

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