A nice group structure on the orbit space of unimodular rows-II

Abstract

We establish an Excision type theorem for niceness of group structure on the orbit space of unimodular rows of length $n$ modulo elementary action. This permits us to establish niceness for relative versions of results for the cases when $n = d+1$, $d$ being the dimension of the base algebra. We then study and establish niceness for the case when $n = d$, and also establish a relative version, when the base ring is a smooth affine algebra over an algebraically closed field.