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Operations on orbits of unimodular vectors. (English) Zbl 0592.20053
Let A be an associative commutative ring with 1. Then $GL\sb nA$ and $E\sb nA$ act on the unimodular rows $Um\sb nA\subset A\sp n$. The orbit set $Um\sb nA/E\sb nA$ 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 $Um\sb nA/E\sb nA$ provided $n\ge 3$. He shows that taking the m-power of an entry in $(a\sb 1,...,a\sb n)\in Um\sb nA$ is a well-defined operation $\psi\sb m$ on $Um\sb nA/E\sb nA$, $n\ge 3$.
Reviewer: E.W.Ellers

20G35Linear algebraic groups over adèles and other rings and schemes
Full Text: DOI
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