Displaying similar documents to “Permutation group extension of groupoids.”

On the lattices of quasivarieties of differential groupoids

Aleksandr Kravchenko (2008)

Commentationes Mathematicae Universitatis Carolinae

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The main result of Romanowska A., Roszkowska B., , Demonstratio Math. (1987), no. 1–2, 277–290, provides us with an explicit description of the lattice of varieties of differential groupoids. In the present article, we show that this variety is 𝒬 -universal, which means that there is no convenient explicit description for the lattice of quasivarieties of differential groupoids. We also find an example of a subvariety of differential groupoids with a finite number of subquasivarieties. ...

Homomorphic images of subdirectly irreducible groupoids

David Stanovský (2001)

Commentationes Mathematicae Universitatis Carolinae

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A groupoid H is a homomorphic image of a subdirectly irreducible groupoid G (over its monolith) if and only if H has a smallest ideal.

On varieties of left distributive left idempotent groupoids

David Stanovský (2004)

Discussiones Mathematicae - General Algebra and Applications

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We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity xⁿ ≈ x decomposes as the direct product of its largest idempotent factor and a cycle. Some properties of subdirectly ireducible LDLI groupoids are found.