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F-quasigroups and generalized modules

Tomáš Kepka·Michael Kinyon·J. D. Phillips
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Abstract

In math.GR/0510298, 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 equational class of (pointed) F-quasigroups and the equational class corresponding to a certain notion of generalized module (with noncommutative, nonassociative addition) for an associative ring.

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Tomáš Kepka, Michael Kinyon, J. D. Phillips. 2005-12-12. F-quasigroups and generalized modules. https://arxiv.org/abs/math/0512244

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