Non-stable K;-theory for QB-rings

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Abstract

We study the class of QB-rings that satisfy the weak cancellation condition of separativity for finitely generated projective modules. This property turns out to be crucial for proving that all (quasi-)invertible matrices over a QB-ring can be diagonalised using row and column operations. The main two consequences of this fact are: (i) The natural map GL1(R) → K1 (R) is surjective, and (ii) the only obstruction to lift invertible elements from a quotient is of K -theoretical nature. We also show that for a reasonably large class of QB-rings that includes the prime ones, separativity always holds.
Original languageEnglish
Pages (from-to)265-300
JournalMathematica Scandinavica
Volume100
Issue number2
DOIs
Publication statusPublished - 1 Jan 2007

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