Distributive groupoids are symmetric-by-medial: An elementary proof
We present an elementary proof (purely in equational logic) that distributive groupoids are symmetric-by-medial.
Distributive implication groupoids
We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.
Enumerating left distributive groupoids
Externally Induced Operations.
Finite AG-groupoid with left identity and left zero.
Finite monogenic distributive systems
Finite simple zeropotent paramedial groupoids
The study of paramedial groupoids (with emphasis on the structure of simple paramedial groupoids) was initiated in [1] and continued in [2], [3] and [5]. The aim of the present paper is to give a full description of finite simple zeropotent paramedial groupoids (i.e., of finite simple paramedial groupoids of type (II)—see [2]). A reader is referred to [1], [2], [3] and [7] for notation and various prerequisites.
Free groupoids with axioms of the form and/or .
Free groupoids with . II.
Generalized fuzzy interior ideals in Abel-Grassmann's groupoids.
Group conjugation has non-trivial LD-identities
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.
Groupoïdes résidués et demi-groupes nomaux
Groupoids and the associative law I. (Associative triples)
Groupoids and the associative law II. (Groupoids with small semigroup distance)
Groupoids and the associative law III. (Szász-Hájek groupoids)
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))