# Article

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Keywords:
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:
[1] Bruck R.H.: A Survey of Binary Systems. Springer, 1971. MR 0093552 | Zbl 0141.01401
[2] Bruck R.H., Paige L.: Loops in which every inner mapping is an automorphism. Ann. of Math. 63 (1956), 308-323. DOI 10.2307/1969612 | MR 0076779
[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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