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Proceedings of the American Mathematical Society

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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: 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.


References [Enhancements On Off] (What's this?)

  • [1] H. Bass, Algebraic K-theory, Benjamin, New York, 1968. MR 0249491 (40:2736)
  • [2] H. Bass, A. Heller and R. G. Swan, The Whitehead group of a polynomial extension, Inst. Haute Études Sci. Publ. Math. No. 22 (1964), 61-79. MR 30 #4806. MR 0174605 (30:4806)
  • [3] S. M. Gersten, On Mayer-Vietoris functors and algebraic K-theory, J. Algebra 18 (1971). MR 0280570 (43:6290)
  • [4] M. Karoubi and O. Villamayor, Foncteurs $ {K^n}$ en algèbre et en topologie, C. R. Acad. Sci. Paris Sér. A-B 269 (1969), 416-419. MR 0251717 (40:4944)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0294452-X
Keywords: Algebraic K-theory, Laurent polynomials, loop and path rings, left regular ring
Article copyright: © Copyright 1971 American Mathematical Society

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