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A group structure on squares

Author(s): Ravi A. Rao; Selby Jose
Journal: Proc. Amer. Math. Soc. 136 (2008), 1181-1191.
MSC (2000): Primary 13C10, 15A04, 19G12
Posted: December 27, 2007
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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: 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
Posted: December 27, 2007
Communicated by: Paul Goerss
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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