A short direct characterization of GS-quasigroups
The theorem about the characterization of a GS-quasigroup by means of a commutative group in which there is an automorphism which satisfies certain conditions, is proved directly.
A Single Groupoid Identity for Steiner Loops
A structure theorem for sets of lengths
A theorem on entropic groupoids
A tree as a finite nonempty set with a binary operation
A (finite) acyclic connected graph is called a tree. Let be a finite nonempty set, and let be the set of all trees with the property that is the vertex set of . We will find a one-to-one correspondence between and the set of all binary operations on which satisfy a certain set of three axioms (stated in this note).
Abelizations of weakly associative hyperstructures based on their direct squares
About the heart of a hypergroup
Addition and correction to the paper "Diagonal algebras"
Affine Gelfand-Dickey Brackets and Holomorphic Vector Bundles.
Affine regular decagons in GS-quasigroup.
Affine regular decagons in GS-quasigroup
In this article the “geometric” concept of the affine regular decagon in a general GS–quasigroup is introduced. The relationships between affine regular decagon and some other geometric concepts in a general GS–quasigroup are explored. The geometrical presentation of all proved statements is given in the GS–quasigroup .
Affine regular icosahedron circumscribed around the affine regular octahedron in GS--quasigroup
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...
Algebraic aspects of web geometry
Algebraic aspects of web geometry, namely its connections with the quasigroup and loop theory, the theory of local differential quasigroups and loops, and the theory of local algebras are discussed.
Algebras of multiplace functions.
Algorithm for the complement of orthogonal operations
G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a -tuple of orthogonal -ary operations, where , to an -tuple of orthogonal -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a -tuple of orthogonal -ary operations to an -tuple of orthogonal -ary operations and an algorithm for complementing a -tuple of orthogonal -ary operations to an -tuple of orthogonal -ary operations. Also we find some...
Almost associative operations generating a minimal clone
Characterizations of 'almost associative' binary operations generating a minimal clone are given for two interpretations of the term 'almost associative'. One of them uses the associative spectrum, the other one uses the index of nonassociativity to measure how far an operation is from being associative.
Almost Periodic Functions on Hypergroups.
Almost Trivial Groupoids
A-loops close to code loops are groups
Let be a diassociative A-loop which is centrally nilpotent of class 2 and which is not a group. Then the factor over the centre cannot be an elementary abelian 2-group.
An algebraic characterization of geodetic graphs
We say that a binary operation is associated with a (finite undirected) graph (without loops and multiple edges) if is defined on and if and only if , and for any , . In the paper it is proved that a connected graph is geodetic if and only if there exists a binary operation associated with which fulfils a certain set of four axioms. (This characterization is obtained as an immediate consequence of a stronger result proved in the paper).