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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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On $K_ 3$ of truncated polynomial rings
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by Janet Aisbett PDF
Trans. Amer. Math. Soc. 294 (1986), 517-536 Request permission


Group homology spectral sequences are used to investigate ${K_3}$ of truncated polynomial rings. If $F$ is a finite field of odd characteristic, we show that relative ${K_2}$ of the pair $(F\left [ t \right ]/({t^q}), ({t^k}))$, which has been identified by van der Kallen and Stienstra, is isomorphic to ${K_3}(F\left [ t \right ]/({t^k}), (t))$ when $q$ is sufficiently large. We also show that ${H_3}({\text {SL}} {\mathbf {Z}}\left [ t \right ]/({t^k});{\mathbf {Z}}) = {{\mathbf {Z}}^{k - 1}} \oplus {\mathbf {Z}}/24$ and is isomorphic to the associated ${K_3}$ group modulo an elementary abelian $2$-group.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 517-536
  • MSC: Primary 18F25; Secondary 13D15, 19D55, 20G10, 20J06
  • DOI:
  • MathSciNet review: 825719