Effective Dimension of Finite Semigroups

Decidability and Tameness in the Theory of Finite Semigroups

Classification of Monogenic Ternary Semigroups

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

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), 128–160, motivated by the Prime Decomposition Theorem of K. Krohn and J. Rhodes, Algebraic theory of machines, I: Prime decomposition theorem for finite semigroups and machines, Transactions of the Ameri...

On the Graphs Related to Green Relations of Finite Semigroups

In this paper we develop an analog of the notion of the con- jugacy graph of  nite groups for the  nite semigroups by considering the Green relations of a  nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a  nite semigroup S , we  first atte...

On the Krohn-rhodes Complexity of Semigroups of Upper Triangular Matrices

We consider the Krohn-Rhodes complexity of certain semigroups of upper triangular matrices over finite fields. We show that for any n > 1 and finite field k, the semigroups of all n × n upper triangular matrices over k and of all n × n unitriangular matrices over k have complexity n− 1. A consequence is that the complexity c > 1 of a finite semigroup places a lower bound of c+1 on the dimension...