Advertisement

algebra universalis

, Volume 43, Issue 2–3, pp 259–268 | Cite as

Finite semigroups with slowly growing pn-sequences

  • Siniša Crvenković
  • Igor Dolinka
  • 25 Downloads

Abstract.

The p n -sequence of a semigroup S is said to be polynomially bounded, if there exist a positive constant c and a positive integer r such that the inequality p n (S) ≤cn r holds for all n≥ 1. In this paper, we fully describe all finite semigroups having polynomially bounded p n -sequences. First we give a characterization in terms of identities satisfied by these semigroups. In the sequel, this result will allow an insight into the structure of such semigroups. We are going to deal with certain ideals and the construction of ideal extension of semigroups. In addition, we supply an effective procedure for deciding whether a finite semigroup has polynomially bounded p n -sequence and give some examples.

Keywords

Positive Integer Effective Procedure Finite Semigroup Ideal Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag Basel, 2000

Authors and Affiliations

  • Siniša Crvenković
    • 1
  • Igor Dolinka
    • 2
  1. 1.University of Novi Sad, Faculty of Science, Institute of Mathematics, Trg Dositeja Obradovića 4, 21000 Novi Sad, Yugoslavia, e-mail: sima@eunet.yuYU
  2. 2.University of Novi Sad, Faculty of Science, Institute of Mathematics, Trg Dositeja Obradovića 4, 21000 Novi Sad, Yugoslavia, e-mail: dockie@unsim.ns.ac.yuYU

Personalised recommendations