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In this paper, we study the K-theory of triangular rings. As an application, we show that for a locally triangular order Λ, the p-torsion in the higher class group Cl2n(Λ) can only occur for primes p which lie under the prime ideals ℘ of [Formula: see text], at which Λ is not maximal.

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Introduction.Let R be a Dedekind domain with quotient field L, A any R-order in a semi-simple L-algebra Z. Define SG,(A) as the kernel of the canonical map Gn(A)~ Gn(Z) and SKn(A ) as the kernel of the canonical map K,(A)-*K,(2). Note that if A is a maximal order, then SG,(A)=SK,(A). In [5], it was proved that if L is a p-adic field with integers R, and F is the maximal R-order in a semisimple L-algebra X, then SKi(F)=0 if and only if Z is a direct product of matrix algebras over fields i.e. SKi(F)=0 if and only if 2; is unramified over its centre. We prove in this paper that for all n>l, SKi~_I(F)=O if and only if 2; is unramified over its centre. This result applies notably in the case F=R~, Z=Lrc