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Presolid varieties of n-semigroups

Avapa Chantasartrassmee, Jörg Koppitz (2005)

Discussiones Mathematicae - General Algebra and Applications

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 by Koppitz...

Pre-solid varieties of semigroups

K. Denecke, Jörg Koppitz (1995)

Archivum Mathematicum

Pre-hyperidentities generalize the concept of a hyperidentity. A variety V is said to be pre-solid if every identity in V is a pre-hyperidentity. Every solid variety is pre-solid. We consider pre-solid varieties of semigroups which are not solid, determine the smallest and the largest of them, and some elements in this interval.

Pre-strongly solid varieties of commutative semigroups

Sarawut Phuapong, Sorasak Leeratanavalee (2011)

Discussiones Mathematicae - General Algebra and Applications

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 greatest pre-strongly...

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