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By a relational system we mean a couple $(A, R)$ where $A$ is a set and $R$ is a binary relation on $A$ , i.e. $R \subseteq A \times A$ . To every directed relational system $𝒜 = (A, R)$ we assign a groupoid $𝒢 (𝒜) = (A, \cdot)$ on the same base set where $x y = y$ if and only if $(x, y) \in R$ . We characterize basic properties of $R$ by means of identities satisfied by $𝒢 (𝒜)$ and show how homomorphisms between those groupoids are related to certain homomorphisms of relational systems.

Groupoids with non-associative triples on the diagonal

Aleš Drápal (1985)

Czechoslovak Mathematical Journal

Groups, transversals, and loops

Tuval Foguel (2000)

Commentationes Mathematicae Universitatis Carolinae

A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.

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Groupoids and the associative law IIIA. (Primitive extensions of SH-groupoids and their semigroup distances)

Groupoids and the associative law IV. (Szász-Hájek Groupoids of Type (A, B, A))

Groupoids and the associative law IX. (Associative triples in some classes of groupoids)

Groupoids and the associative law V. (Szász-Hájek groupoids fo type (A, A, B))

Groupoids and the associative law VI. (Szász-Hájek groupoids of type (a, b, c))

Groupoids and the associative law. VII. Semigroup distance of SH-groupoids

Groupoids and the associative law VIIA. (SH-groupoids of type (A, B, A) and their semigroup distances)

Groupoids and the associative law XII. (Representable cardinal functions)

Groupoids assigned to relational systems

Groupoids with non-associative triples on the diagonal

Groups, transversals, and loops

Grupoids and the associative law VII B (SH-grupoids and simply generated congruences)

Grupoidy a grupy s operátory

GS-quasigroups

Currently displaying 21 – 34 of 34