A group structure on squares

Rao, Ravi; Jose, Selby

doi:10.1090/S0002-9939-07-09065-X

A group structure on squares
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by Ravi A. Rao and Selby Jose

Proc. Amer. Math. Soc. 136 (2008), 1181-1191

DOI: https://doi.org/10.1090/S0002-9939-07-09065-X

Published electronically: 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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