Abstarct: In this thesis, we show that if a ring R satisfies unit 1-stable range, then so does Mn(R) for any n ≥ 1. If R has many unit-regular elements, then so does Mn(R) for any n ≥ 1. Also we prove if R satisfies G − M condition, then so does Mn(R) for any n ≥ 1. Then we study SB-rings. We will give necessary and sufficient conditions under which a semilocal ring is a SB-ring. Furthermore, we extend these results to exchange rings with all primitive factors artinian. For such rings, we observe that the concept of SB-ring coincides with G-M condition.