Exercise 12, § 11

Tag 00E3, permanent. Cite it as [Bourbaki, Tag 00E3].

Algebra, VIII, p. 210

Let $f: A\rightarrow B$ be a surjective ring homomorphism, $\mathfrak{a}$ its kernel, and $i$ the canonical injection of $\mathfrak{a}$ into A. Construct a homomorphism $\partial : K_1(B)\rightarrow K_0(\mathfrak{a})$ such that the sequence

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K_1(A)\longrightarrow^fK_1(B)\longrightarrow^{\partial}K_0(\mathfrak{a})\longrightarrow^iK_0(A)\longrightarrow^fK_0(B)

is exact (argue as in Exercise 11, c)).

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Cites

Exercise 11