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.

Full text not available from this repository.

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

Downloads: Statistics Overview

## 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 |

Related URLs: | |

Identification Number: | |

Last Modified: | 22 Mar 2012 14:27 |

Deposited On: | 22 Mar 2012 13:58 |

Repository Staff Only: item control page