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Resumen de Non-stable [K]-theory for [QB] -rings

Pere Ara Árbol académico, Francesc Perera Domènech Árbol académico

  • 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 ofK-theoretical nature.We also show that for a reasonably large class of QB-rings that includes the prime ones, separativity always holds.

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