## Abstract

For a semigroup S, p(n)(S) denotes the number of n-ary term operations of S depending on all their variables. The purpose of this paper is to study finite semigroups S with the property that their p(n)-sequence p(S) = <p0(S), p1(S),...> is bounded. Such semigroups are described first in terms of identities and then structurally as nilpotent extensions of semilattices, Boolean groups and rectangular bands. As a corollary it is shown that if p(S) is bounded then eventually either p(n)(S)= 0 or 1. It is also shown that there is an effective procedure which decides whether the p(n)-sequence of a given finite semigroup is bounded or not. (C) 2001 Elsevier Science B.V. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 205-214 |

Number of pages | 10 |

Journal | Journal of Pure and Applied Algebra |

Volume | 157 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 23 Mar 2001 |

## Keywords

- ALGEBRAS