A note on Bol loops of order 2nk.
A note on compatible reflexive relations on quasigroups
A Note on Fuzzy Groups
A note on hypervector spaces
The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.
A note on loops of square-free order
Let be a loop such that is square-free and the inner mapping group is nilpotent. We show that is centrally nilpotent of class at most two.
A note on -groups for .
A note on quasi and bi-duals in ternary semigroups.
A note on -groupoids
A note on simple medial quasigroups
A solvable primitive group with finitely generated abelian stabilizers is finite.
A note on simple quasigroups
A note on subdirectly irreducible groupoids
A note on the finite extensivity property
A note on the number of associative triples in finite commutative Moufang loops
A note on the number of associative triples in quasigroups isotopic to groups
A note on uniserial loops
All ordinal numbers with the following property are found: there exists a loop such that its subloops form a chain of ordinal type .
A note on WA-quasigroups
A parallelogram configuration condition in nets
After describing a (general and special) coordinatization of -nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in -nets with small degree .
A realization of -groups
A remark on -systems in groups
A scoop from groups: equational foundations for loops
Groups are usually axiomatized as algebras with an associative binary operation, a two-sided neutral element, and with two-sided inverses. We show in this note that the same simplicity of axioms can be achieved for some of the most important varieties of loops. In particular, we investigate loops of Bol-Moufang type in the underlying variety of magmas with two-sided inverses, and obtain ``group-like'' equational bases for Moufang, Bol and C-loops. We also discuss the case when the inverses are only...