The Study Of Three Classes Transformation Semigroups With N-element Permutation

Let Xn={1,2,…,n} ordered in the standard way.Let Pn(Tn)be the semigroup of partial(full)transformations of the set Xn.Let Ln be the symmetric inverse semigroup on Xn.Let An(Sn)be the alternating(symmetric)group on Xn.Let Singn=Tn\Sn be the semigroup of all singular transformations of the set Xn,then Singn be the subsemigroup of Tn.Let LSn=Ln\Sn be the semigroup of all partial one to one transformations of the set Xn,then LSn be the subsemigroup of Ln.Let ASn=An?Singn,then ASn be the subsemigroup of Tn.let ALSn=An?LSn,then ALSn be the subsemigroup of Ln.we say that a transformation ? in Pn is order-preserving(order-reversing)if x?y implies x??y?(x??y?),for all x,y ?dom?.Let POn(PDn)be the semigroup of partial order-preserving(order-reversing)transformation of the set Xn.Let PDOn=POn?PDn,then PDOn be the subsemigroup of Pn.In this thesis,we introduce the transformation semigroup with n-element permutation ASn,ALSn,? PDOn.The main results are given in follwing:we study the rank and maximal subsemigroup of semigroup ASn,where the rank of semigroup.ASn is equal to 3,and the maximal subsemigroup ASn has and only has M1=ASn\?n-1and M2G ? Singn types.The rank of semigroup ALSn and ALS(n,r)is equal to 3.we characterize the Green relations of the semigroups of PDOn and obtain that the rank of ideals non group elements in semigroups PDOn is NGrank(MD(n,r))=Nidrank(MD(n,r))=rank(MD(n,r))=(?)The correlation rank of ideals in semigroup PDOn is...