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F-quasigroup; Moufang loop; generalized modules
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.
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