Do you want to publish a course? Click here

Periodic elements of the free idempotent generated semigroup on a biordered set

135   0   0.0 ( 0 )
 Added by Mark Sapir
 Publication date 2008
  fields
and research's language is English




Ask ChatGPT about the research

We show that every periodic element of the free idempotent generated semigroup on an arbitrary biordered set belongs to a subgroup of the semigroup.



rate research

Read More

133 - Luis Oliveira 2012
In this paper we present a new embedding of a semigroup into a semiband (idempotent-generated semigroup) of depth 4 (every element is the product of 4 idempotents) using a semidirect product construction. Our embedding does not assume that S is a monoid (although it assumes a weaker condition), and works also for (non-monoid) regular semigroups. In fact, this semidirect product is particularly useful for regular semigroups since we can defined another embedding for these semigroups into a smaller semiband of depth 2. We shall then compare our construction with other known embeddings, and we shall see that some properties of S are preserved by our embedding.
69 - Tara Brough 2020
An improvement on earlier results on free products of automaton semigroups; showing that a free product of two automaton semigroups is again an automaton semigroup providing there exists a homomorphism from one of the base semigroups to the other. The result is extended by induction to give a condition for a free product of finitely many automaton semigroups to be an automaton semigroup.
The enhanced power graph $mathcal P_e(S)$ of a semigroup $S$ is a simple graph whose vertex set is $S$ and two vertices $x,y in S$ are adjacent if and only if $x, y in langle z rangle$ for some $z in S$, where $langle z rangle$ is the subsemigroup generated by $z$. In this paper, first we described the structure of $mathcal P_e(S)$ for an arbitrary semigroup $S$. Consequently, we discussed the connectedness of $mathcal P_e(S)$. Further, we characterized the semigroup $S$ such that $mathcal P_e(S)$ is complete, bipartite, regular, tree and null graph, respectively. Also, we have investigated the planarity together with the minimum degree and independence number of $mathcal P_e(S)$. The chromatic number of a spanning subgraph, viz. the cyclic graph, of $mathcal P_e(S)$ is proved to be countable. At the final part of this paper, we construct an example of a semigroup $S$ such that the chromatic number of $mathcal P_e(S)$ need not be countable.
In this paper we introduce the Schutzenberger category $mathbb D(S)$ of a semigroup $S$. It stands in relation to the Karoubi envelope (or Cauchy completion) of $S$ in the same way that Schutzenberger groups do to maximal subgroups and that the local divisors of Diekert do to the local monoids $eSe$ of $S$ with $ein E(S)$. In particular, the objects of $mathbb D(S)$ are the elements of $S$, two objects of $mathbb D(S)$ are isomorphic if and only if the corresponding semigroup elements are $mathscr D$-equivalent, the endomorphism monoid at $s$ is the local divisor in the sense of Diekert and the automorphism group at $s$ is the Schutzenberger group of the $mathscr H$-class of $S$. This makes transparent many well-known properties of Greens relations. The paper also establishes a number of technical results about the Karoubi envelope and Schutzenberger category that were used by the authors in a companion paper on syntactic invariants of flow equivalence of symbolic dynamical systems.
The cyclic graph $Gamma(S)$ of a semigroup $S$ is the simple graph whose vertex set is $S$ and two vertices $x, y$ are adjacent if the subsemigroup generated by $x$ and $y$ is monogenic. In this paper, we classify the semigroup $S$ such that whose cyclic graph $Gamma(S)$ is complete, bipartite, tree, regular and a null graph, respectively. Further, we determine the clique number of $Gamma(S)$ for an arbitrary semigroup $S$. We obtain the independence number of $Gamma(S)$ if $S$ is a finite monogenic semigroup. At the final part of this paper, we give bounds for independence number of $Gamma(S)$ if $S$ is a semigroup of bounded exponent and we also characterize the semigroups attaining the bounds.
comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا