Tom\'a\v s Kepka, Michael K. Kinyon, J.D. Phillips
F-quasigroups and generalized modules

Comment.Math.Univ.Carolin. 49,2 (2008) 249-257.

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