F-quasigroups and generalized modules

Tomáš Kepka; Michael K. Kinyon; Jon D. Phillips

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 2, page 249-257
  • ISSN: 0010-2628

Abstract

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In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, J. Algebra 317 (2007), 435–461, we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the class of (pointed) F-quasigroups and the class corresponding to a certain notion of generalized module (with noncommutative, nonassociative addition) for an associative ring.

How to cite

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Kepka, Tomáš, Kinyon, Michael K., and Phillips, Jon D.. "F-quasigroups and generalized modules." Commentationes Mathematicae Universitatis Carolinae 49.2 (2008): 249-257. <http://eudml.org/doc/250460>.

@article{Kepka2008,
abstract = {In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, J. Algebra 317 (2007), 435–461, we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the class of (pointed) F-quasigroups and the class corresponding to a certain notion of generalized module (with noncommutative, nonassociative addition) for an associative ring.},
author = {Kepka, Tomáš, Kinyon, Michael K., Phillips, Jon D.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {F-quasigroup; Moufang loop; generalized modules; Moufang loops; NK-loops; F-quasigroups; generalized modules},
language = {eng},
number = {2},
pages = {249-257},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {F-quasigroups and generalized modules},
url = {http://eudml.org/doc/250460},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Kepka, Tomáš
AU - Kinyon, Michael K.
AU - Phillips, Jon D.
TI - F-quasigroups and generalized modules
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 2
SP - 249
EP - 257
AB - In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, J. Algebra 317 (2007), 435–461, we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the class of (pointed) F-quasigroups and the class corresponding to a certain notion of generalized module (with noncommutative, nonassociative addition) for an associative ring.
LA - eng
KW - F-quasigroup; Moufang loop; generalized modules; Moufang loops; NK-loops; F-quasigroups; generalized modules
UR - http://eudml.org/doc/250460
ER -

References

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  1. Bruck R.H., A Survey of Binary Systems, Springer, 1971. Zbl0141.01401MR0093552
  2. Bruck R.H., Paige L., 10.2307/1969612, Ann. of Math. 63 (1956), 308-323. (1956) MR0076779DOI10.2307/1969612
  3. Kepka T., Kinyon M.K., Phillips J.D., 10.1016/j.jalgebra.2007.05.007, J. Algebra 317 (2007), 435-461. (2007) Zbl1133.20051MR2362925DOI10.1016/j.jalgebra.2007.05.007
  4. Moufang R., 10.1007/BF01448037, Math. Ann. 110 (1935), 416-430. (1935) MR1512948DOI10.1007/BF01448037
  5. Pflugfelder H.O., Quasigroups and Loops: Introduction, Helderman, Berlin, 1990. Zbl0715.20043MR1125767

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