The Green's Relation for Semigroup of Preserving an E~* Relation and Orientation Partial One-one Transformations
Long Wei-fen · Journal of Guangxi Normal University · 2014
Let IXbe the symmetric inverse semigroup on the finite set Xand Ean equivalence on X.Let IE*(X)={f∈IX :for arbitrary elements x,y ∈dom(f),(x,y)∈Eif and only if(f(x),f(y))∈E}.Then IE*(X)forms an inverse subsemigroup of IX.If X is a totally ordered set and E is convex equivalence on X,then let OPIE*(X)be a semigroup consisting of all preserving orientation partial oneone transformations in IE*(X).It is a new class of semigroup and its research is difficult and complicated.By studying it,some new structure and properties of semigroups are explored.Green's relations on OPIE*(X)are described in this paper.