ON THE SUPERDIMENSIONS OF RELATIVELY FREE NILPOTENT SEMIGROUPS

2004 ◽  
Vol 14 (05n06) ◽  
pp. 773-784
Author(s):  
L. M. SHNEERSON
Keyword(s):  
Semigroup Variety ◽  
Free Objects ◽  
Free Semigroups

We prove that in the variety of nilpotent semigroups of class ≤2, which is defined by the Neumann–Taylor identity xyzyx=yxzxy, the sequence of the superdimensions for relatively free semigroups is convergent to 1 and at the same time every element of the sequence is strictly less than 1. This gives the first example of a semigroup variety for which the set of superdimensions for the free objects is infinite.

ON MAXIMAL SUBGROUPS OF FREE OBJECTS OF CERTAIN COMPLETELY REGULAR SEMIGROUP VARIETIES

2011 ◽  
Vol 21 (03) ◽  
pp. 473-484
Author(s):  
IGOR DOLINKA
Keyword(s):  
Regular Semigroup ◽  
Semigroup Variety ◽  
Maximal Subgroups ◽  
Completely Regular Semigroup ◽  
Locally Finite ◽  
Completely Regular ◽  
Free Generators ◽  
Free Semigroups ◽  
Semigroup Varieties ◽  
Relatively Free Group

By adjusting a method of Kadourek and Polák developed for free semigroups satisfying xr ≏ x, we prove that if [Formula: see text] is a periodic group variety, then any maximal subgroup of the free object in the completely regular semigroup variety of the form [Formula: see text] is a relatively free group in [Formula: see text] over a suitable set of free generators. When [Formula: see text] is locally finite, we provide some bounds for the sizes of its finitely generated members.

scholarly journals Relatively Free Semigroups of Intermediate Growth

2001 ◽  
Vol 235 (2) ◽  
pp. 484-546 ◽  
Author(s):  
L.M Shneerson
Keyword(s):  
Intermediate Growth ◽  
Free Semigroups

Completely simple semigroups: free products, free semigroups and varieties

1981 ◽  
Vol 88 (3-4) ◽  
pp. 293-313 ◽  
Author(s):  
P. R. Jones
Keyword(s):  
Matrix Representation ◽  
Maximal Subgroups ◽  
Lattice Of Varieties ◽  
Free Products ◽  
Completely Simple Semigroups ◽  
Countable Rank ◽  
Free Semigroups ◽  
Abelian Subgroups ◽  
And Inversion ◽  
Completely Simple

SynopsisThe class CS of completely simple semigroups forms a variety under the operations of multiplication and inversion (x−1 being the inverse of x in its ℋ-class). We determine a Rees matrix representation of the CS-free product of an arbitrary family of completely simple semigroups and deduce a description of the free completely simple semigroups, whose existence was proved by McAlister in 1968 and whose structure was first given by Clifford in 1979. From this a description of the lattice of varieties of completely simple semigroups is given in terms of certain subgroups of a free group of countable rank. Whilst not providing a “list” of identities on completely simple semigroups it does enable us to deduce, for instance, the description of all varieties of completely simple semigroups with abelian subgroups given by Rasin in 1979. It also enables us to describe the maximal subgroups of the “free” idempotent-generated completely simple semigroups T(α, β) denned by Eberhart et al. in 1973 and to show in general the maximal subgroups of the “V-free” semigroups of this type (which we define) need not be free in any variety of groups.

Group-Free Semigroups

2001 ◽  
pp. 227-258
Author(s):  
P. A. Grillet
Keyword(s):  
Free Semigroups

Left large subsets of free semigroups and groups that are not right large

2014 ◽  
Vol 90 (2) ◽  
pp. 374-385 ◽  
Author(s):  
Neil Hindman ◽  
Lakeshia Legette Jones ◽  
Monique Agnes Peters
Keyword(s):  
Free Semigroups

Free Objects in the Category of Completely Distributive Lattices

2020 ◽  
pp. 129-150
Author(s):  
Karl H. Hofmann ◽  
Michael Mislove
Keyword(s):  
Distributive Lattices ◽  
Free Objects ◽  
Completely Distributive

GRAVITATIONAL BAG EFFECTS ON KALUZA KLEIN AND STRING EXCITATIONS

1989 ◽  
Vol 04 (19) ◽  
pp. 5119-5131 ◽  
Author(s):  
E. I. GUENDELMAN
Keyword(s):  
Extra Dimensions ◽  
Blow Up ◽  
Point Of View ◽  
Spherically Symmetric ◽  
Massive String ◽  
Free Objects ◽  
Higher Dimensional ◽  
Central Regions ◽  
The Masses ◽  
Kaluza Klein

Gravitational Bags are spherically symmetric solutions of higher-dimensional Kaluza Klein (K – K) theories, where the compact dimensions become very large near the center of the geometry, although they are small elsewhere. The K – K excitations therefore become very light when located near the center of this geometry and this appears to affect drastically the naive tower of the masses spectrum of K – K theories. In the context of string theories, string excitations can be enclosed by Gravitational Bags, making them not only lighter, but also localized, as observed by somebody, that does not probe the central regions. Strings, however, can still have divergent sizes, as quantum mechanics seems to demand, since the extra dimensions blow up at the center of the geometry. From a projected 4-D point of view, very massive string bits may lie inside their Schwarzschild radii, as pointed out by Casher, Gravitational Bags however are horizon free objects, so no conflict with macroscopic causality arises if the string excitations are enclosed by Gravitational Bags.

scholarly journals FREE ADEQUATE SEMIGROUPS

2011 ◽  
Vol 91 (3) ◽  
pp. 365-390 ◽  
Author(s):  
MARK KAMBITES
Keyword(s):  
Inverse Semigroup ◽  
Word Problem ◽  
Explicit Description ◽  
Finitely Generated ◽  
Free Objects ◽  
Ample Semigroup ◽  
Free Inverse Semigroup ◽  
Adequate Semigroup

AbstractWe give an explicit description of the free objects in the quasivariety of adequate semigroups, as sets of labelled directed trees under a natural combinatorial multiplication. The morphisms of the free adequate semigroup onto the free ample semigroup and into the free inverse semigroup are realised by a combinatorial ‘folding’ operation which transforms our trees into Munn trees. We use these results to show that free adequate semigroups and monoids are 𝒥-trivial and never finitely generated as semigroups, and that those which are finitely generated as (2,1,1)-algebras have decidable word problem.

scholarly journals Saturated and epimorphically closed varieties of semigroups

1984 ◽  
Vol 36 (2) ◽  
pp. 153-175 ◽  
Author(s):  
P. M. Higgins
Keyword(s):  
Semigroup Variety ◽  
Necessary Condition

AbstractWe establish a necessary condition (E) for a semigroup variety to be closed under the taking of epimorphisms and a necessary condition (S) for a variety to consist entirely of saturated semigroups. Condition (S) is shown to be sufficient for heterotypical varieties and a stronger condition (S′) is shown to be sufficient for homotypical varieties.

scholarly journals Random walks of infinite moment on free semigroups

2019 ◽  
Vol 175 (3-4) ◽  
pp. 1099-1122
Author(s):  
Behrang Forghani ◽  
Giulio Tiozzo
Keyword(s):  
Random Walks ◽  
Free Semigroups
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