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Transactions of the American Mathematical Society

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

 
 

 

On $K_ 3$ of truncated polynomial rings


Author: Janet Aisbett
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
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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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Article copyright: © Copyright 1986 American Mathematical Society