Displaying similar documents to “Pre-solid varieties of semigroups”

Pre-strongly solid varieties of commutative semigroups

Sarawut Phuapong, Sorasak Leeratanavalee (2011)

Discussiones Mathematicae - General Algebra and Applications

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Generalized hypersubstitutions are mappings from the set of all fundamental operations into the set of all terms of the same language do not necessarily preserve the arities. Strong hyperidentities are identities which are closed under the generalized hypersubstitutions and a strongly solid variety is a variety which every its identity is a strong hyperidentity. In this paper we give an example of pre-strongly solid varieties of commutative semigroups and determine the least and the...

M-Solid Subvarieties of some Varieties of Commutative Semigroups

Koppitz, J. (1997)

Serdica Mathematical Journal

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∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung. The basic concepts are M -hyperidentities, where M is a monoid of hypersubstitutions. The set of all M -solid varieties of semigroups forms a complete sublattice of the lattice of all varieties of semigroups. We fix some specific varieties V of commutative semigroups and study the set of all M -solid subvarieties of V , in particular, if V is nilpotent.

Presolid varieties of n-semigroups

Avapa Chantasartrassmee, Jörg Koppitz (2005)

Discussiones Mathematicae - General Algebra and Applications

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he class of all M-solid varieties of a given type t forms a complete sublattice of the lattice ℒ(τ) of all varieties of algebrasof type t. This gives a tool for a better description of the lattice ℒ(τ) by characterization of complete sublattices. In particular, this was done for varieties of semigroups by L. Polák ([10]) as well as by Denecke and Koppitz ([4], [5]). Denecke and Hounnon characterized M-solid varieties of semirings ([3]) and M-solid varieties of groups were characterized...