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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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

Abstract:

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: https://doi.org/10.1090/S0002-9947-1986-0825719-7
  • MathSciNet review: 825719