Geodesic
F-quasigroups and generalized modules
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 249-257.

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In Kepka T., Kinyon M.K., Phillips J.D., {\it The structure of F-quasigroups\/}, J. Algebra {\bf 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.
Classification : 16Y99, 17A30, 20N05
Keywords: F-quasigroup; Moufang loop; generalized modules 
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Kepka, Tomáš; Kinyon, Michael K.; Phillips, J. D. F-quasigroups and generalized modules. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 249-257. http://geodesic.mathdoc.fr/item/CMUC_2008__49_2_a6/