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Group conjugation has non-trivial LD-identities

Aleš Drápal, Tomáš Kepka, Michal Musílek (1994)

Commentationes Mathematicae Universitatis Carolinae

We show that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.

Groupoids assigned to relational systems

Ivan Chajda, Helmut Länger (2013)

Mathematica Bohemica

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 A × A . To every directed relational system 𝒜 = ( A , R ) we assign a groupoid 𝒢 ( 𝒜 ) = ( A , · ) on the same base set where x y = y if and only if ( x , y ) 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.

Grupoidy a grupy s operátory

Ladislav Sedláček (1961)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica-Physica-Chemica

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