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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The $ K$-theory of triangular matrix rings. II


Author: M. E. Keating
Journal: Proc. Amer. Math. Soc. 100 (1987), 235-236
MSC: Primary 18F25; Secondary 16A54, 19D45
MathSciNet review: 884458
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Abstract: Let $ T$ be the upper triangular matrix ring defined by a pair of rings $ R$ and $ S$ and an $ R - S$-bimodule $ M$. We use the QP definition of algebraic $ K$-theory to give a quick proof that the homomorphism

$\displaystyle {\pi _m}:{K_m}(T) \to {K_m}(R) \oplus {K_m}(S),\quad m \geqslant 0,$

induced by the obvious ring epimorphism is an isomorphism.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0884458-3
PII: S 0002-9939(1987)0884458-3
Keywords: Algebraic $ K$-theory, triangular matrix ring
Article copyright: © Copyright 1987 American Mathematical Society