On the $K$-theory of Laurent polynomials
Author:
S. M. Gersten
Journal:
Proc. Amer. Math. Soc. 30 (1971), 223-228
MSC:
Primary 18F25
DOI:
https://doi.org/10.1090/S0002-9939-1971-0294452-X
MathSciNet review:
0294452
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Abstract | References | Similar Articles | Additional Information
Abstract: The Karoubi-Villamayor K-theory of the ring of Laurent polynomials over a regular ring is computed. It is shown that Milnor’s ${K_2}$ of a ring of Laurent polynomials over a regular ring maps onto ${K_1}$ of the ring.
- Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
- H. Bass, A. Heller, and R. G. Swan, The Whitehead group of a polynomial extension, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 61–79. MR 174605
- S. M. Gersten, On Mayer-Vietoris functors and algebraic $K$-theory, J. Algebra 18 (1971), 51–88. MR 280570, DOI https://doi.org/10.1016/0021-8693%2871%2990127-X
- Max Karoubi and Orlando Villamayor, Foncteurs $K^{n}$ en algèbre et en topologie, C. R. Acad. Sci. Paris Sér. A-B 269 (1969), A416–A419 (French). MR 251717
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Additional Information
Keywords:
Algebraic <I>K</I>-theory,
Laurent polynomials,
loop and path rings,
left regular ring
Article copyright:
© Copyright 1971
American Mathematical Society
