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Keywords:
F-quasigroup; Moufang loop; generalized modules
F-quasigroup; Moufang loop; generalized modules
Summary:
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.
References:
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[3] Kepka T., Kinyon M.K., Phillips J.D.: The structure of F-quasigroups. J. Algebra 317 (2007), 435-461. DOI 10.1016/j.jalgebra.2007.05.007 | MR 2362925 | Zbl 1133.20051
[4] Moufang R.: Zur Struktur von Alternativkörpern. Math. Ann. 110 (1935), 416-430. DOI 10.1007/BF01448037 | MR 1512948
[5] Pflugfelder H.O.: Quasigroups and Loops: Introduction. Helderman, Berlin, 1990. MR 1125767 | Zbl 0715.20043
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