K1of separative exchange rings and C*-algebras with real rank zero

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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...

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ژورنال

عنوان ژورنال: Pacific Journal of Mathematics

سال: 2000

ISSN: 0030-8730

DOI: 10.2140/pjm.2000.195.261