Synthesis Theorem for Finite Regular Semigroups, and Its Generalization.

摘要

The Synthesis Theorem describes the global structure of a semigroup and gives its multiplication in 'coordinate form'. Rees' theorem and the Krohn-Rhodes theorem are special cases. The theorem holds for all finite semigroups and also for a rather general class of infinite semigroups. This theorem has two special properties: 1) It coordinates a semigroup globally (i.e., it describes how any two elements are multiplied); 2) It is general: It applies to all finite semigroups and to a large class of infinite semigroups. Keywords: Reprints. (kr)