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M-Solid Subvarieties of some Varieties of Commutative Semigroups

Koppitz, J. (1997)

Serdica Mathematical Journal

∗ 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.

Near heaps

Ian Hawthorn, Tim Stokes (2011)

Commentationes Mathematicae Universitatis Carolinae

On any involuted semigroup ( S , · , ' ) , define the ternary operation [ a b c ] : = a · b ' · c for all a , b , c ∈ S . The resulting ternary algebra ( S , [ ] ) satisfies the para-associativity law [ [ a b c ] d e ] = [ a [ d c b ] e ] = [ a b [ c d e ] ] , which defines the variety of semiheaps. Important subvarieties include generalised heaps, which arise from inverse semigroups, and heaps, which arise from groups. We consider the intermediate variety of near heaps, defined by the additional laws [ a a a ] = a and [ a a b ] = [ b a a ] . Every Clifford semigroup is a near heap when viewed as a semiheap, and we show that the Clifford semigroup...

Notes on semimedial semigroups

Fitore Abdullahu, Abdullah Zejnullahu (2009)

Commentationes Mathematicae Universitatis Carolinae

The class of semigroups satisfying semimedial laws is studied. These semigroups are called semimedial semigroups. A connection between semimedial semigroups, trimedial semigroups and exponential semigroups is presented. It is proved that the class of strongly semimedial semigroups coincides with the class of trimedial semigroups and the class of dimedial semigroups is identical with the class of exponential semigroups.

On modular elements of the lattice of semigroup varieties

Boris M. Vernikov (2007)

Commentationes Mathematicae Universitatis Carolinae

A semigroup variety is called modular if it is a modular element of the lattice of all semigroup varieties. We obtain a strong necessary condition for a semigroup variety to be modular. In particular, we prove that every modular nil-variety may be given by 0-reduced identities and substitutive identities only. (An identity u = v is called substitutive if the words u and v depend on the same letters and v may be obtained from u by renaming of letters.) We completely determine all commutative modular...

On permutability in semigroup varieties

Bedřich Pondělíček (1991)

Mathematica Bohemica

The paper contains characterizations of semigroup varieties whose semigroups with one generator (two generators) are permutable. Here all varieties of regular * -semigroups are described in which each semigroup with two generators is permutable.

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