Locality of DS and associated varieties

@article{Jones1995LocalityOD,
  title={Locality of DS and associated varieties},
  author={Peter R. Jones and Peter G. Trotter},
  journal={Journal of Pure and Applied Algebra},
  year={1995},
  volume={104},
  pages={275-301}
}
The Globals of Some Subpseudovarieties of DA
TLDR
Using the word problem for free pro- monoids, it is shown that the bilateral semidirect product is local, where denotes the pseudovariety of all finite semilattices.
On the Equation
This note uses some recent powerful tools related with semidirect products * of pseu-dovarieties of semigroups, particularly when the second factor is the pseudovariety of all finite groups, to give
On the equation V G = EV
This note uses some recent powerful tools related with semidirect products V W of pseu-dovarieties of semigroups, particularly when the second factor is the pseudovariety G of all nite groups, to
On the equation V*G=EV
The G-Exponent of a Pseudovariety of Semigroups*
Abstract Ash's proof of the Pointlike Conjecture provides an algorithm for calculating the group-pointlike subsets of a finite semigroup S. We denote by PG(S) the subsemigroup of P(S), the elements
GLOBALS OF PSEUDOVARIETIES OF COMMUTATIVE SEMIGROUPS: THE FINITE BASIS PROBLEM, DECIDABILITY AND GAPS
Abstract Whereas pseudovarieties of commutative semigroups are known to be finitely based, the globals of monoidal pseudovarieties of commutative semigroups are shown to be finitely based (or of
A Structural Approach to the Locality of Pseudovarieties of the Form LH (m) V
We show that if H is a Fitting pseudovariety of groups and V is a local pseudovariety of monoids, then LH ⓜ V is local if either V contains the six element Brandt monoid, or H is a non-trivial
The lattice of pseudovarieties of idempotent semigroups and a non-regular analogue
Abstract. We use classical results on the lattice $ \cal L (\cal B) $ of varieties of band (idempotent) semigroups to obtain information on the structure of the lattice Ps (DA) of subpseudovarieties
Semidirect products of regular semigroupsPeter
Within the usual semidirect product S T of regular semigroups S and T lies the set Reg (S T) of its regular elements. Whenever S or T is completely simple, Reg (S T) is a (regular) subsemigroup. It
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References

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Implicit operations on DS
TLDR
This work illustrates how the study of the topological semigroups ΩnV (for a pseudovariety V) can be useful to the knowledge of V and finds factorizations of implicit operations in terms of regular and explicit ones.
Mal'cev products of varieties of completely regular semigroups
Abstract Whilst the Mal'cev product of completely regular varieties need not again be a variety, it is shown that in many important instances a variety is in fact obtained. However, unlike the
Varieties of Finite Categories
TLDR
The main goal is to point out the similarities and distinctions between C-varieties and varieties of finite monoids that underlie the more traditional approach to the theory.
On semi-groups in which xr = x
  • J. Green, D. Rees
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1952
In this note we are concerned with the semi-group Snr, generated by n of its elements, in which each element x satisfies the equation xr = x, the semi-group being otherwise free. The main result
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