Isotopic invariants of natural planar ternary rings
In the paper the invariant (geometrical) character of some properties of natural planar ternary rings is shown by using isotopic transformations.
Kleinsche Geometrie und Theorie der geometrischen Objekte
Moufang planes and the groups EK6 and SL2(K), K a Cayley division algebra.
Natural planar ternary rings
New closure conditions and some problems in loop theory.
On a generalization of nets
On Groupoids Having a Linear Congruence Class Geometry.
On Rusakov’s -ary -groups
Properties of -ary groups connected with the affine geometry are considered. Some conditions for an -ary -group to be derived from a binary group are given. Necessary and sufficient conditions for an -ary group -derived from an additive group of a field to be an -group are obtained. The existence of non-commutative -ary -groups which are not derived from any group of arity for every , is proved.
On the geometry of field extensions.
On the planar translation structures
One configurational characterization of Ostrom nets
Bz the quadrileteral condition in a given net there is meant the following implication: If are arbitrary points, no three of them lie on the same line, with coll (collinearity) for any five from six couples then there follows the collinearity coll for the remaining couple . In the article there is proved the every net satisfying the preceding configuration condition is necessarity the Ostrom net (i.e., the net over a field). Conversely, every Ostrom net satisfies the above configuration...
One generalization of quasifield
Places of alternative fields
Planare Neokörper mit additiven Kürzungsregeln.
Produkte von Kongruenzklassengeometrien universeller Algebren.
Quadratische Semi-Ordnungen und Quadratische Formen.
Reflection loops of spaces with congruence and hyperbolic incidence structure
In an absolute space with congruence there are line reflections and point reflections. With the help of point reflections one can define in a natural way an addition + of points which is only associative if the product of three point reflection is a point reflection again. In general, for example for the case that is a linear space with hyperbolic incidence structure, the addition is not associative. is a K-loop or a Bruck loop.
Regularity of algebras with applications to congruence class geometry
Ternary rings with a left quasi-zero belonging to translation planes
Translation structures and group partitions