J. Andre constructed a skewaffine structure as a group space of a normally transitive group. In this paper his construction is used to describe the structure of the set of circles not passing through a point of a Laguerre plane. Sufficient conditions to ensure that this structure is a skewaffine plane are given.
The concept of the affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be introduced in this paper. The theorem of the unique determination of the affine regular icosahedron by means of its four vertices which satisfy certain conditions will be proved. The connection between affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be researched. The geometrical representation of the introduced concepts and relations between them...
We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients. The main example, we consider outside vector spaces, concerns Boolean algebras,...
We proved in an earlier work that any existence variety of regular algebras is generated by its simple unital Artinian members, while any existence variety of Arguesian sectionally complemented lattices is generated by its simple members of finite length. A characterization of the class of simple unital Artinian members [members of finite length, respectively] of such varieties is given in the present paper.