Weak group inverses and partial isometries in proper *-rings

A weak group element is introduced in a proper *-ring. Several equivalent conditions of elements are investigated. We prove that an pseudo core invertible if it both partial isometry and invertible. Reverse order law additive property the inverse presented. Finally, under certain assumption on a, a◯Wa∗=a∗a◯W presented by using normality part its group-EP decomposition.