Chapter 1. Extension of the fundamental theorem of finite semigroups

  title={Chapter 1. Extension of the fundamental theorem of finite semigroups},
  author={Price E. Stiffler},
  journal={Advances in Mathematics},
Decidability of complexity one-half for finite semigroups
ResumeAll semigroups considered are finite. The semigroup C is by definition combinatorial (or group free or aperiodic) iff the maximal subgroups of C are singletons. Let S2oS1 denote the wreath
Weakly Iterated Block Products and Applications to Logic and Complexity
Characterizing for any pseudovarieties of monoids U, V the smallest Pseudovariety W that contains U and such that W □ V = W allows us to obtain new decomposition results for a number of important varieties such as DA, DO and DA * G.
Locality and Centrality: The Variety ZG
It is shown that ZG is local, that is, the semidirect product ZG ∗ D of ZG by definite semigroups is equal to LZG, the variety of semig groups where all local monoids are in ZG.
An effective lower bound for group complexity of finite semigroups and automata
The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, Complexity of finite semigroups, Annals of Mathematics (2) 88 (1968),
On the equation V*G=EV
Quivers of monoids with basic algebras
Abstract We compute the quiver of any finite monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a
The structure of finite monoids satisfying the relation ℛ = ℋ
It is shown that any finite monoid S on which Green’s relations R and H coincide divides the monoid of all upper triangular row-monomial matrices over a finite group. The proof is constructive; given