Displaying similar documents to “The lattice of varieties and pseudovarieties of band monoids.”

The Galois correspondence between subvariety lattices and monoids of hpersubstitutions

Klaus Denecke, Jennifer Hyndman, Shelly L. Wismath (2000)

Discussiones Mathematicae - General Algebra and Applications

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Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence. ...

Maximal submonoids of monoids of hypersubstitutions

Ilinka Dimitrova, Jörg Koppitz (2006)

Discussiones Mathematicae - General Algebra and Applications

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For a monoid M of hypersubstitutions, the collection of all M-solid varieties forms a complete sublattice of the lattice L(τ) of all varieties of a given type τ. Therefore, by the study of monoids of hypersubstitutions one can get more insight into the structure of the lattice L(τ). In particular, monoids of hypersubstitutions were studied in [9] as well as in [5]. We will give a complete characterization of all maximal submonoids of the monoid Reg(n) of all regular hypersubstitutions...