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Geoodular axiomatics of affine spaces. (English) Zbl 0881.20030
The author proves in a purely algebraic way that any flat geoodular space is an affine space and vice versa. This result gives a new axiomatics of affine spaces based on the concept of vectorization centered at a point (being a vector space) and on two identities describing the relation between vectorizations centered at any two points. Such an approach admits a useful treatment in the frame of universal algebras.
MSC:
20N05 Loops, quasigroups
51A25 Algebraization in linear incidence geometry
22A30 Other topological algebraic systems and their representations
53B05 Linear and affine connections
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