Abstract: Yong Shao

Locally Inverse Semigroup with Inverse Transversals

 

           Suppose that S is a locally inverse semigroup with an inverse transversal S◦. We can construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We obtain the new characterization of the natural partial order on S and equivalent characterization of locally inverse semigroup with an Clifford transversal. If S is a locally inverse semigroup with an Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.