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.
Keywords: F-quasigroup, Moufang loop, generalized modules
AMS Subject Classification: 20N05