The holomorphic automorphism group of the complex disk.
The hyperbolic square and Möbius transformations.
The hyperbolic triangle centroid
Some gyrocommutative gyrogroups, also known as Bruck loops or K-loops, admit scalar multiplication, turning themselves into gyrovector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry. In classical mechanics the centroid of a triangle in velocity space is the velocity of the center of momentum of three massive objects with equal masses located at the triangle vertices. Employing gyrovector space techniques we find...
The hyperrings of order 3.
The ideal structure of simple ternary algebras
The inner mappings of extra loops
The lattice of solid -subgroups of a retractable group
The Levitzki Radical for Omega-groups
The Levitzki radical for -groups.
The local integration of Leibniz algebras
This article gives a local answer to the coquecigrue problem for Leibniz algebras, that is, the problem of finding a generalization of the (Lie) group structure such that Leibniz algebras are the corresponding tangent algebra structure. Using links between Leibniz algebra cohomology and Lie rack cohomology, we generalize the integration of a Lie algebra into a Lie group by proving that every Leibniz algebra is isomorphic to the tangent Leibniz algebra of a local Lie rack. This article ends with...
The minimal extension of sequences III. On problem 16 of Grätzer and Kisielewicz
The main result of this paper is a description of totally commutative idempotent groupoids. In particular, we show that if an idempotent groupoid (G,·) has precisely m ≥ 2 distinct essentially binary polynomials and they are all commutative, then G contains a subgroupoid isomorphic to the groupoid described below. In [2], this fact was proved for m = 2.
The number of minimal varieties of idempotent groupoids
The operation in operator algebras
The binary operation , called Jordan triple product, and its variants (such as e.g. the sequential product or the inverted Jordan triple product ) appear in several branches of operator theory and matrix analysis. In this paper we briefly survey some analytic and algebraic properties of these operations, and investigate their intimate connection to Thompson type isometries in different operator algebras.
The set of hypergroups with operators which are constructed from a set with two elements
The structure of hemigroups.
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 tensor product of groupoids
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