Of Separative Exchange Rings and C * - Algebras with Real Rank Zero

Separative Exchange Rings and C * - Algebras with Real Rank Zero

For any (unital) exchange ring R whose finitely 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 GL1(R) → K1(R) is surjective. In combination with a result of Huaxin Lin, it follow...

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

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 ...

Lifting Units modulo Exchange Ideals and C∗-algebras with Real Rank Zero

Given a unital ring R and a two-sided ideal I of R, we consider the question of determining when a unit of R/I can be lifted to a unit of R. For the wide class of separative exchange ideals I, we show that the only obstruction to lifting invertibles relies on a K-theoretic condition on I. This allows to extend previously known index theories to this context. Using this we can draw consequences ...

A note on lifting projections

Suppose $pi:mathcal{A}rightarrow mathcal{B}$ is a surjective unital $ast$-homomorphism between C*-algebras $mathcal{A}$ and $mathcal{B}$, and $0leq aleq1$ with $ain  mathcal{A}$. We give a sufficient condition that ensures there is a proection $pin mathcal{A}$ such that $pi left( pright) =pi left( aright) $. An easy consequence is a result of [L. G. Brown and G. k. Pedersen, C*-algebras of real...

Separative Ideals of Exchange Rings