Notes on AT-algebras and extensions of AT-algebras by K

H. Lin and H. Su classified AT-algebras of real rank zero. An AT-algebra often becomes an extension of an AT-algebra by an AF-algebra. In this paper, we define a new invariant pi(A) of C*-algebra A by partial isometries and give a necessary condition on which a C*-algebra is an AT-algebra. We demonstrate that there is an essential extension of an AT-algebra with real rank zero by K which is not an AT-algebra.