Semigroup Forum

, Volume 57, Issue 2, pp 208–239

Operators on the Lattice of Pseudovarieties of Finite Semigroups

  • Norman R. Reilly
  • Shuhua Zhang

DOI: 10.1007/PL00005974

Cite this article as:
Reilly, N. & Zhang, S. Semigroup Forum (1998) 57: 208. doi:10.1007/PL00005974


(F) of pseudovarieties of finite semigroups that attempts to take full advantage of the underlying lattice structure, Auinger, Hall and the present authors recently introduced fourteen complete congruences on L (F). Such congruences provide a framework from which to study L (F) both locally and globally. For each such congruence ρ and each UL (F) the ρ-class of U is an interval [Uρ, Uρ]. This provides a family of operators of the form UUρ on L (F) that reveal important relationships between elements of L (F). Various aspects of these operators are considered including characterizations of Uρ, bases of pseudoidentities for Uρ, instances of commutativity (Uρ)σ = Uσ)ρ, as well as the semigroups generated by certain pairs of such operators.

Copyright information

© 1998 Springer-Verlag New York Inc.

Authors and Affiliations

  • Norman R. Reilly
  • Shuhua Zhang

There are no affiliations available