EXTENSIONS OF INDUCTIVE LIMITS OF CIRCLE ALGEBRAS

A classic result of L. G. Brown [3] and G. Elliott [7] says that every extension of two AF-algebras is again an AF-algebra. We generalize th is result to the larger class of C-algebras which are inductive limit s of circle algebras and have real rank zero. Let E be an extension of C-algebras A and B, 0-->A-->E-->B-->0, where A and B have real rank zero and are inductive limits of circle algebras. If E has red rank ze ro and stable rank one, then it is an inductive limit of circle algebr as. Moreover, E has real rank zero and is an inductive limit of circle algebras if and only if the extension satisfies the condition that th e index maps K-j(B)-->K-1-j(A) for j = 0, 1, are zero.