From relation to emulation: the covering lemma for transformation semigroups
Author
Nehaniv, C.L.
Attention
2299/3172
Abstract
We define the kernel of a relational morphism of finite or infinite, faithful or non-faithful transformation semigroups. We prove the covering lemma for transformation semigroups, and a wreath product embedding theorem in terms of this kernel. Applications easily obtained using this new language include a global embedding theorem for right simple semigroups without idempotents, a proof of the Krohn-Rhodes theorem, and some results about transformation groups.