Quadratic Level Quasigroup Equations With Four Variables II: the Lattice of Varieties
Qualgebras and knotted 3-valent graphs
This paper is devoted to new algebraic structures, called qualgebras and squandles. Topologically, they emerge as an algebraic counterpart of knotted 3-valent graphs, just like quandles can be seen as an "algebraization" of knots. Algebraically, they are modeled after groups with conjugation and multiplication/squaring operations. We discuss basic properties of these structures, and introduce and study the notions of qualgebra/squandle 2-cocycles and 2-coboundaries. Knotted 3-valent graph invariants...
Quantum idempotence, distributivity, and the Yang-Baxter equation
Quantum quasigroups and loops are self-dual objects that provide a general framework for the nonassociative extension of quantum group techniques. They also have one-sided analogues, which are not self-dual. In this paper, natural quantum versions of idempotence and distributivity are specified for these and related structures. Quantum distributive structures furnish solutions to the quantum Yang-Baxter equation.
Quasetrivial and nearly quasitrivial distributive goupoids and semigroups
Quasigroup automorphisms and symmetric group characters
The automorphisms of a quasigroup or Latin square are permutations of the set of entries of the square, and thus belong to conjugacy classes in symmetric groups. These conjugacy classes may be recognized as being annihilated by symmetric group class functions that belong to a -ideal of the special -ring of symmetric group class functions.
Quasigroup covers of division groupoids
Let be a division groupoid that is not a quasigroup. For each regular cardinal we construct a quasigroup on that is a quasigroup cover of (i.e., is a homomorphic image of and is not an image of any quasigroup that is a proper factor of ). We also show how to easily obtain quasigroup covers from free quasigroups.
Quasigroups and Factorisation of Complete Digraphs
Quasigroups and tactical systems.
Quasigroups arisen by right nuclear extension
The aim of this paper is to prove that a quasigroup with right unit is isomorphic to an -extension of a right nuclear normal subgroup by the factor quasigroup if and only if there exists a normalized left transversal to in such that the right translations by elements of commute with all right translations by elements of the subgroup . Moreover, a loop is isomorphic to an -extension of a right nuclear normal subgroup by a loop if and only if is middle-nuclear, and there exists...
Quasigroups determined by balanced identities of length
Quasigroups having at most three inner mappings
Quasigroups, isotopic to a group
Quasigroups of fractions
Quasigroups satisfying balanced but not Belousov equations are group isotopes.
Quasigroups which are unions of three proper subquasigroups
Quasigroups which satisfy certain generalized forms of the Abelian identity
Quasigroups whose regular mappings are automorphisms
Quasimodules generated by three elements
Quasitrivial left distributive groupoids
Left distributive quasitrivial groupoids are completely described and those of them which are subdirectly irreducible are found. There are also determined all left distributive algebras such that is a quasitrivial groupoid.
Quotients and homomorphisms of relational systems
Relational systems containing one binary relation are investigated. Quotient relational systems are introduced and some of their properties are characterized. Moreover, homomorphisms, strong mappings and cone preserving mappings are introduced and the interplay between these notions is considered. Finally, the connection between directed relational systems and corresponding groupoids is investigated.