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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Commutator automorphisms of formal power series rings


Authors: Joseph Gubeladze and Zaza Mushkudiani
Journal: Proc. Amer. Math. Soc. 134 (2006), 1569-1578
MSC (2000): Primary 13J10, 13F25, 19A99, 19B99
Published electronically: October 28, 2005
MathSciNet review: 2204266
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Abstract | References | Similar Articles | Additional Information

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: http://dx.doi.org/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
Published electronically: October 28, 2005
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.