Operations on orbits of unimodular vectors
Let A be an associative commutative ring with 1. Then \(GL_ nA\) and \(E_ nA\) act on the unimodular rows \(Um_ nA\subset A^ n\). The orbit set \(Um_ nA/E_ nA\) is the set of unimodular rows modulo the addition operations over A. The author introduces an action of the multiplicative semigroup of the integers on the set \(Um_ nA/E_ nA\) provided \(n\geq 3\). He shows that taking the m-power of an entry in \((a_ 1,...,a_ n)\in Um_ nA\) is a well-defined operation \(\psi_ m\) on \(Um_ nA/E_ nA\), \(n\geq 3\).
scientific article; zbMATH DE number 3950844
scientific article