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
By a relational system we mean a couple where is a set and is a binary relation on , i.e. . To every directed relational system we assign a groupoid on the same base set where if and only if . We characterize basic properties of by means of identities satisfied by and show how homomorphisms between those groupoids are related to certain homomorphisms of relational systems.
Grupoids and the associative law VII B (SH-grupoids and simply generated congruences)
Grupoidy a grupy s operátory
Homomorphic images of subdirectly irreducible groupoids
A groupoid is a homomorphic image of a subdirectly irreducible groupoid (over its monolith) if and only if has a smallest ideal.
Ideals in selfdistributive groupoids
Products of (left) ideals in selfdistributive groupoids are studied.
Inclusion properties of the intersection convolution of relations.
Infinite simple zeropotent paramedial groupoids
The paper is an immediate continuation of [3], where one can find various notation and other useful details. In the present part, a full classification of infinite simple zeropotent paramedial groupoids is given.
Inflations of the AG-groupoids.
-groupoids: Algebraic and topological properties of special groupoids. (-Gruppoide: Algebraische und topologische Eigenschaften spezieller Gruppoide.)
Le théorème de Jordan-Hölder dans certains groupoïdes ordonnés
Left-distributive embedding algebras.
Left-Garside categories, self-distributivity, and braids
In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the relationship between the self-distributivity law LD and braids amounts to the result that a certain category associated with LD is a left-Garside category, which projects onto the standard Garside category of braids. This approach leads to a realistic program for establishing the Embedding Conjecture of [Dehornoy, Braids and...
Medial idempotent groupoids. I
Modular posets and semigroups.
Multiple left distributive systems
We describe the free objects in the variety of algebras involving several mutually distributive binary operations. Also, we show how an associative operation can be constructed on such systems in good cases, thus obtaining a two way correspondence between LD-monoids (sets with a left self-distributive and a compatible associative operation) and multi-LD-systems (sets with a family of mutually distributive operations).
Nets Associated to Multigroupoids.
Nets Associated to Multigroupoids. (Short Communication).