T-quasigroups (Part II.)
Transitive groupoids
Transitivity, Associativity and Bisymmetry eputations on GD- goupoids.
Transitivity, Associativity And Bisymmetry Equations On GD-Groupoids
Travel groupoids
In this paper, by a travel groupoid is meant an ordered pair such that is a nonempty set and is a binary operation on satisfying the following two conditions for all : Let be a travel groupoid. It is easy to show that if , then if and only if . We say that is on a (finite or infinite) graph if and Clearly, every travel groupoid is on exactly one graph. In this paper, some properties of travel groupoids on graphs are studied.
Travel groupoids on infinite graphs
The notion of travel groupoids was introduced by L. Nebeský in 2006 in connection with a study on geodetic graphs. A travel groupoid is a pair of a set and a binary operation on satisfying two axioms. We can associate a graph with a travel groupoid. We say that a graph has a travel groupoid if the graph associated with the travel groupoid is equal to . Nebeský gave a characterization of finite graphs having a travel groupoid. In this paper, we study travel groupoids on infinite graphs....
Trilinear constructions of quasimodules
Trimedial quasigroups and generalized modules I.
Two enumeration principles for free algebras
Two-generated idempotent groupoids with small clones
A characterization of all classes of idempotent groupoids having no more than two essentially binary term operations with respect to small finite models is given.
UAI- лупы Осборна
Über die Stirlingschen Zahlen der zweiten Art.
Une classe de quasi-groupes qui peuvent servir à représenter des «moyennes»
Unions of subquasigroups
Unipotent quasigroups
Uniqueness of Steiner laws on cubic curves.
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...
Universal cyclic relations
Varieties of abelian quasigroups
Varieties of groupoids associated with involuted restrictive bisemigroups of binary relations.