Wreath products of algebras: Generalizing the Krohn-Rhodes theorem to arbitrary algebras
The Krohn-Rhodes Prime Decomposition Theorem describes the basic semigroups needed in a wreath product decomposition of a finite semigroup. The author's goal has been to extend this famous theorem to arbitrary finite algebras, and for this purpose possible generalizations of the central notions of the Krohn-Rhodes theory, such as wreath products, the corresponding decompositions, aperiodicity and solvability, are defined and studied. Difficulties associated with the generalization are pinpointed and some open problems are posed. Connections with the Hobby-McKenzie theory of tame congruences are also noted. The paper is actually an extended abstract of the author's dissertation, and hence all proofs and many details have been omitted.
Krohn-Rhodes prime decomposition theorem
scientific article; zbMATH DE number 836811