The 𝐾-theory of triangular matrix rings. II

Keating, M. E.

doi:10.1090/S0002-9939-1987-0884458-3

The $K$-theory of triangular matrix rings. II
HTML articles powered by AMS MathViewer

by M. E. Keating PDF

Proc. Amer. Math. Soc. 100 (1987), 235-236 Request permission

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 \[ {\pi _m}:{K_m}(T) \to {K_m}(R) \oplus {K_m}(S),\quad m \geqslant 0,\] induced by the obvious ring epimorphism is an isomorphism.

References

A. J. Berrick and M. E. Keating, The $K$-theory of triangular matrix rings, Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 69–74. MR 862629, DOI 10.1090/conm/055.1/862629
R. Keith Dennis and Susan C. Geller, $K_{i}$ of upper triangular matrix rings, Proc. Amer. Math. Soc. 56 (1976), 73–78. MR 404392, DOI 10.1090/S0002-9939-1976-0404392-5
M. E. Keating, The $K$-theory of triangular rings and orders, Algebraic $K$-theory, number theory, geometry and analysis (Bielefeld, 1982) Lecture Notes in Math., vol. 1046, Springer, Berlin, 1984, pp. 178–192. MR 750681, DOI 10.1007/BFb0072022
Daniel Quillen, Higher algebraic $K$-theory. I, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Lecture Notes in Math., Vol. 341, Springer, Berlin, 1973, pp. 85–147. MR 0338129