The structure of hemigroups. (Short Communication).
The table of characters of some quasigroups
It is known that (ℤₙ,-ₙ) are examples of entropic quasigroups which are not groups. In this paper we describe the table of characters for quasigroups (ℤₙ,-ₙ).
The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry
In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.
The totally simple quasigroups
The upper triangular algebra loop of degree
A natural loop structure is defined on the set of unimodular upper-triangular matrices over a given field. Inner mappings of the loop are computed. It is shown that the loop is non-associative and nilpotent, of class 3. A detailed listing of the loop conjugacy classes is presented. In particular, one of the loop conjugacy classes is shown to be properly contained in a superclass of the corresponding algebra group.
Torsion quasimodules
Towards a geometric theory for left loops
In [Mwambene E., Multiples of left loops and vertex-transitive graphs, Cent. Eur. J. Math. 3 (2005), no. 2, 254–250] it was proved that every vertex-transitive graph is the Cayley graph of a left loop with respect to a quasi-associative Cayley set. We use this result to show that Cayley graphs of left loops with respect to such sets have some properties in common with Cayley graphs of groups which can be used to study a geometric theory for left loops in analogy to that for groups.
T-quasigroups (Part I.)
T-quasigroups (Part II.)
Transitivity, Associativity and Bisymmetry eputations on GD- goupoids.
Transitivity, Associativity And Bisymmetry Equations On GD-Groupoids
Trilinear constructions of quasimodules
Trimedial quasigroups and generalized modules I.
Two enumeration principles for free algebras
UAI- лупы Осборна
Une classe de quasi-groupes qui peuvent servir à représenter des «moyennes»
Unions of subquasigroups
Unipotent quasigroups
Units in quasigroups with classical Bol--Moufang type identities
We proceed with Kunen's research about existence of units (left, right, two-sided) in quasigroups with classical Bol--Moufang type identities, listed in paper Extra loops II, by F. Fenyves (1969). We consider those Bol--Moufang identities where it has not been decided yet whether a quasigroup fulfilling this identity has to possess a left or right identity. We also provide a table of all Moufang--Bol identities, indicating at each whether it describes the variety of groups, and whether it forces...
Varieties of abelian quasigroups