Simple generalized inductive limits of C*-algebras

We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C~*-algebra. We also show that if a unital C~*-algebra can be approximately embedded into some tensorially self absorbing C~*-algebra C(e.g., uniformly hyperfinite(UHF)-algebras of infinite type, the Cuntz algebra O_2),then we can construct a simple separable unital generalized inductive limit. When C is simple and infinite(resp.properly infinite), the construction is also infinite(resp. properly infinite). When C is simple and approximately divisible, the construction is also approximately divisible. When C is a UHF-algebra and the connecting maps satisfy a trace condition, the construction has tracial rank zero.