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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0574499-1
PII: S 0002-9939(1980)0574499-1
Keywords: Excision, algebraic K-theory, Kähler differentials
Article copyright: © Copyright 1980 American Mathematical Society