Representation of undirected graphs by anticommutative conservative groupoids
The paper studies tolerances and congruences on anticommutative conservative groupoids. These groupoids can be assigned in a one-to-one way to undirected graphs.
Retracts of monounary algebras corresponding to groupoids
Right division in Moufang loops
If is a group, and the operation is defined by then by direct verification is a quasigroup which satisfies the identity . Conversely, if one starts with a quasigroup satisfying the latter identity the group can be constructed, so that in effect is determined by its right division operation. Here the analogous situation is examined for a Moufang loop. Subtleties arise which are not present in the group case since there is a choice of defining identities and the identities produced by...
Rot-Quasigroups
Rot-quasigroups as isotopes of Abelian groups
Rough semigroups and rough fuzzy semigroups based on fuzzy ideals
In this paper, we firstly introduce a special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S. Then we define the lower and upper approximations based on a fuzzy ideal in semigroups. We can establish rough semigroups, rough ideals, rough prime ideals, rough fuzzy semigroups, rough fuzzy ideals and rough fuzzy prime ideals according to the definitions of rough sets and rough fuzzy sets. Furthermore, we shall consider the relationships among semigroups and rough semigroups,...
Schreier loops
We study systematically the natural generalization of Schreier's extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.
Secure two-way on-line communication by using quasigroup enciphering with almost public key.
Selfdistributive groupoids of small orders
After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial.
Selfdistributive groupoids. Part A1. Non-indempotent left distributive groupoids
Selfdistributive groupoids. Part D1: Left distributive semigroups
Selfdistributive grupoids, Part A2: Non-idempotent left distributive quasigroups
Self-invariant 1-factorizations of complete graphs and finite Bol loops of exponent 2.
Self-orthogonal cyclic n-quasigroups.
Self-orthogonal cyclic n-quasigroups. (Short Communication).
Semigroup representations of medial groupoids
Semi-ipergruppi e ipergruppi -completi
Semisymmetrization and Mendelsohn quasigroups
The semisymmetrization of an arbitrary quasigroup builds a semisymmetric quasigroup structure on the cube of the underlying set of the quasigroup. It serves to reduce homotopies to homomorphisms. An alternative semisymmetrization on the square of the underlying set was recently introduced by A. Krapež and Z. Petrić. Their construction in fact yields a Mendelsohn quasigroup, which is idempotent as well as semisymmetric. We describe it as the Mendelsohnization of the original quasigroup. For quasigroups...
Separable Quasigroups.
Several aspects on the hypergroups associated with -ary relations.