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

 

A group structure on squares


Authors: Ravi A. Rao and Selby Jose
Journal: Proc. Amer. Math. Soc. 136 (2008), 1181-1191
MSC (2000): Primary 13C10, 15A04, 19G12
Published electronically: December 27, 2007
MathSciNet review: 2367092
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that there is an abelian group structure on the orbit set of ``squares'' of unimodular rows of length $ n$ over a commutative ring of stable dimension $ d$ when $ d = 2n - 3$, $ n$ odd and also an abelian group structure on the orbit set of ``fourth powers'' of unimodular rows of length $ n$ over a commutative ring of stable dimension $ d$ when $ d = 2n - 3$, $ n$ even.


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Additional Information

Ravi A. Rao
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Mumbai, India 400 005
Email: ravi@math.tifr.res.in

Selby Jose
Affiliation: Department of Mathematics, Ismail Yusuf College, Jogeshwari(E), Mumbai, India 400-060
Email: selbyjose@rediffmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09065-X
PII: S 0002-9939(07)09065-X
Keywords: Unimodular rows, Suslin matrix, elementary orbit
Received by editor(s): October 5, 2006
Received by editor(s) in revised form: January 8, 2007
Published electronically: December 27, 2007
Communicated by: Paul Goerss
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.