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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
Posted:
December 27, 2007
MathSciNet review:
2367092
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Additional Information
Abstract: We show that there is an abelian group structure on the orbit set of ``squares'' of unimodular rows of length  over a commutative ring of stable dimension  when  ,  odd and also an abelian group structure on the orbit set of ``fourth powers'' of unimodular rows of length  over a commutative ring of stable dimension  when  ,  even.
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- J.F. ADAMS, Vector fields on spheres. Ann. of Math. (2), 75, 603-632 (1962). MR 0139178 (25:2614)
- 2.
- H. BASS, Algebraic
 -theory. W. A. Benjamin, Inc., New York-Amsterdam (1968). MR 0249491 (40:2736)
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- S.M. BHATWADEKAR and RAJA SRIDHARAN, The Euler class group of a Noetherian ring. Compositio Math. 122, no. 2, 183-222 (2000). MR 1775418 (2001g:13018)
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- S.M. BHATWADEKAR and RAJA SRIDHARAN, On Euler classes and stably free projective modules. Algebra, arithmetic and geometry, Part I, II (Mumbai, 2000), 139-158, Tata Inst. Fund. Res. Stud. Math. 16, Tata Inst. Fund. Res., Bombay, 2002. MR 1940666 (2003i:13012)
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- A.S. GADRE and R.A. RAO, A nice group structure on the orbit space of unimodular rows, (preprint 2006), accepted and to appear in K-theory, January 2008.
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- R.A. RAO, The Bass-Quillen conjecture in dimension three but characteristic
 via a question of A. Suslin. Invent. Math. 93, 3, 609-618 (1988). MR 952284 (89d:13011)
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 and WMS of a non-singular affine algebra.  -theory (Strasbourg, 1992). Asterisque no. 226, 11, 411-420 (1994). MR 1317126 (96e:19001)
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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
Posted:
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.
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