Green's relations and regularity of a kind of variants semi-group
Ding He · Journal of Guizhou Normal College · 2012
F-(X)={α∈TX:x∈X,xα≤x} is an order-decreasing transformation semigroup.α∈F-(X)andα an idempotent,then let =T-α(X)={f∈TX:(x,y)∈ker(α)■(xf,yf)∈ker(α)and xfα≤xα},Fix element θ in the semi-group T-α(X)and define an operation° on T-α(X),for an arbitraryf,g∈T-α(X)and f°g=fθg,which is the production of mappings.We refer the semi-group after the new operation as a variant semi-group of T-α(X),denoted by T-α(X;θ).In this paper we discuss the Green's relations and regularity.