Unitification of Weakly p.q.-Baer *-Rings

In this paper, we introduce a concept of weakly principally quasi-Baer *-rings in terms of central cover. We prove that a *-rings is a principally quasi-Baer *-rings if and only if it is weakly principally quasi-Baer *-rings with unity. A partial solution to the problem similar to unitification problem raised by S. K. Berberian is obtained.