Commutator automorphisms of formal power series rings

Gubeladze, Joseph; Mushkudiani, Zaza

doi:10.1090/S0002-9939-05-08221-3

Commutator automorphisms of formal power series rings
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by Joseph Gubeladze and Zaza Mushkudiani PDF

Proc. Amer. Math. Soc. 134 (2006), 1569-1578 Request permission

Abstract:

For a big class of commutative rings $R$, every continuous $R$-automorphism of $R[[X_1,\ldots ,X_n]]$ with the linear part the identity is in the commutator subgroup of $\operatorname {Aut}(R[[X_1,\ldots ,X_n]])$. An explicit bound for the number of commutators involved and a $K$-theoretic interpretation of this result are provided.

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