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The special automorphism group of R[t]/(t(m))[x₁,…,x(n)] and coordinates of a subring of R[t][x₁,…,x(n)]

van den Essen, Arno and Maubach, Stefan and Vénéreau, Stéphane. (2007) The special automorphism group of R[t]/(t(m))[x₁,…,x(n)] and coordinates of a subring of R[t][x₁,…,x(n)]. Journal of pure and applied algebra, Vol. 210, H. 1. pp. 141-146.

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Official URL: http://edoc.unibas.ch/dok/A5248978

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Abstract

Let R be a ring. The Special Automorphism Group SAut(R)R[x(1),..., x(n)] is the set of all automorphisms with determinant of the Jacobian equal to 1. It is shown that the canonical map of SAut(R[t]) R[t][x(1),...,x(n)] to SAutR(m) R-m[x(1),...,x(n)] where R-m := R[t]/(t(m)) and Q subset of R is surjective. This result is used to study a particular case of the following question: if A is a subring of a ring B and f is an element of A vertical bar n vertical bar is a coordinate over B does it imply that f is a coordinate over A? It is shown that if A = R[t(m), t(m+1),...] subset of R[t] = B then the answer to this question is "yes". Also, a question on the Venereau polynomial is settled, which indicates another "coordinate-like property" of this polynomial.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft)
UniBasel Contributors:Vénéreau, Stéphane
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:North-Holland
ISSN:0022-4049
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:22 Mar 2012 14:27
Deposited On:22 Mar 2012 13:58

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