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Distributive implication groupoids

Ivan Chajda, Radomir Halaš (2007)

Open Mathematics

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.

Finite simple zeropotent paramedial groupoids

Jung R. Cho, Tomáš Kepka (2002)

Czechoslovak Mathematical Journal

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.

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.

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