A group structure on squares

Abstract

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.

Nice group structure on the elementary orbit space of unimodular rows

“…In [14,Proposition 3.5], Jose and Rao proved that if R is a reduced affine algebra of dimension d ≥ 2 over an algebraically closed field k, then the group structure on Um d+1 (R)/E d+1 (R) is nice. If (a 0 , a 1 , .…”