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Commutator automorphisms of formal power series rings

Author(s): Joseph Gubeladze; Zaza Mushkudiani
Journal: Proc. Amer. Math. Soc. 134 (2006), 1569-1578.
MSC (2000): Primary 13J10, 13F25, 19A99, 19B99
Posted: October 28, 2005
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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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Additional Information:

Joseph Gubeladze
Affiliation: Department of Mathematics, San Francisco State University, San Francisco, California 94132
Email: soso@math.sfsu.edu

Zaza Mushkudiani
Affiliation: Kavsadze Street 4, Apart. 12, Tbilisi, Republic of Georgia

DOI: 10.1090/S0002-9939-05-08221-3
PII: S 0002-9939(05)08221-3
Keywords: Formal power series ring, retraction, automorphism, commutator
Received by editor(s): January 16, 2004
Received by editor(s) in revised form: January 3, 2005
Posted: October 28, 2005
Communicated by: Bernd Ulrich
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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