TY - JOUR
T1 - From relation to emulation: the covering lemma for transformation semigroups
AU - Nehaniv, C.L.
N1 - Original article can be found at: http://www.sciencedirect.com/science/journal/00224049 Copyright Elsevier B.V. DOI: 10.1016/0022-4049(95)00030-5 [Full text of this article is not available in the UHRA]
PY - 1996
Y1 - 1996
N2 - 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.
AB - 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.
U2 - 10.1016/0022-4049(95)00030-5
DO - 10.1016/0022-4049(95)00030-5
M3 - Article
SN - 0022-4049
VL - 107
SP - 75
EP - 87
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 1
ER -