On the CPO-inverse in *-rings

The notion of the CPO-inverse is extended from the set of all complex nxn matrices of index 1 to the set R(#) of all core invertible elements in a *-ring R with identity. Properties of this generalized inverse are investigated and some known results are thus generalized. We apply the CPO-inverse to introduce two relations on R(#) and prove that they are partial orders. We give several characterizations of these partial orders and explore connections between them and some well-known partial orders.