𝐾₂ measures excision for 𝐾₁

Geller, Susan C.; Weibel, Charles A.

doi:10.1090/S0002-9939-1980-0574499-1

$K_{2}$ measures excision for $K_{1}$
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by Susan C. Geller and Charles A. Weibel PDF

Proc. Amer. Math. Soc. 80 (1980), 1-9 Request permission

Abstract:

Let B be a commutative ring, A a subring of B, and I an ideal of B contained in A. Excision holds if ${K_1}(A,I)$ and ${K_1}(B,I)$ are isomorphic. We show that the obstruction to excision holding is a subquotient of ${K_2}(B/{I^2})$. We then use this obstruction to show that, if A and B are fixed, the excision problem for I has no bearing on the excision problem for ideals contained in I.

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