Green’s Relations for the Variants of Finite E-Order-preserving Partial Transformations Semigroups
Qin Mei-qing · Journal of Hainan Normal University · 2011
Let X be a finite totally ordered set and E be an equivalence on X. Denote PEOPX={α∈PX∶ x,y∈ doma,(x,y)∈E且x≤y (xα,yα)∈E且xα≤yα}. Fix an element θ and define an operation on PEOPX by α°β=αθβ and PEOPX forms a semigroup which is called the variant semigroup of finite E-Order-preserving partial transformations semigroups, and it was denoted as PEOPX(θ). In this paper ,we describe the Green’s relation for the semigroup PEOPX(θ).