Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



$ K\sb{2}$ measures excision for $ K\sb{1}$

Authors: Susan C. Geller and Charles A. Weibel
Journal: Proc. Amer. Math. Soc. 80 (1980), 1-9
MSC: Primary 13D15; Secondary 18F25
MathSciNet review: 574499
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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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Keywords: Excision, algebraic K-theory, Kähler differentials
Article copyright: © Copyright 1980 American Mathematical Society