There is created a retirement system which shall be placed under the management and control of the board for the purposes of providing retirement benefits and other benefits under this chapter for public school employees. It shall be a budget unit of the state government and shall have the power and privileges of a corporation and the right to bring and defend actions and to implead and be impleaded. It shall be known as the "Public School Employees Retirement System," and by such name all of its business shall be transacted, all of its funds shall be invested, and all of its cash, securities, and other property shall be held.