Displaying similar documents to “Cohomology groups of a groupoid.”

On left distributive left idempotent groupoids

Přemysl Jedlička (2005)

Commentationes Mathematicae Universitatis Carolinae

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We study the groupoids satisfying both the left distributivity and the left idempotency laws. We show that they possess a canonical congruence admitting an idempotent groupoid as factor. This congruence gives a construction of left idempotent left distributive groupoids from left distributive idempotent groupoids and right constant groupoids.

The minimal extension of sequences III. On problem 16 of Grätzer and Kisielewicz

J. Dudek (1996)

Colloquium Mathematicae

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The main result of this paper is a description of totally commutative idempotent groupoids. In particular, we show that if an idempotent groupoid (G,·) has precisely m ≥ 2 distinct essentially binary polynomials and they are all commutative, then G contains a subgroupoid isomorphic to the groupoid N m described below. In [2], this fact was proved for m = 2.