Of Separative Exchange Rings Andc * - Algebras with Real Rank Zerop

نویسندگان

  • Huaxin Lin
  • Shuang Zhang
چکیده

For any (unital) exchange ring R whose nitely generated projective modules satisfy the separative cancellation property (A A = A B = B B =) A = B), it is shown that all invertible square matrices over R can be diagonalized by elementary row and column operations. Consequently, the natural homomorphism GL 1 (R) ! K 1 (R) is surjective. In combination with a result of Huaxin Lin, it follows that for any separative, unital C*-algebra A with real rank zero, the topological K 1 (A) is naturally isomorphic to the unitary group U(A) modulo the connected component of the identity. This veriies, in the separative case, a conjecture of Shuang Zhang.

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تاریخ انتشار 1999