• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2011.tde-31082011-110130
Document
Author
Full name
Napoleon Caro Tuesta
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2011
Supervisor
Committee
Levcovitz, Daniel (President)
Coutinho, Severino Collier
Ferreira, Vitor de Oliveira
Ferrero, Miguel Angel Alberto
Tengan, Eduardo
Title in Portuguese
Ideais de anéis de operadores diferenciais
Keywords in Portuguese
Álgebras de Weyl
Anéis de operadores
Ideais
Séries de pot~encias
Teorema de Stafford
Abstract in Portuguese
Em [12] J.T. Stafford demonstrou que todo ideal à esquerda ou à direita da álgebra de Weyl 'A IND. n' (K) = K '[ 'x IND. 1', ...,'x IND. n' ] ' partial IND. 1', ... 'partial IND. n' (K um corpo de característica zero) é gerado por dois elementos. Consideremos o anel 'D IND. n' := K [['x IND.1', ...'x IND. n']] de operadores diferenciais sobre o anel de séries de potências formais K[['x IND. 1';...' xI ND. n']]. Uma pergunta natural é se todo ideal à esquerda ou à direita de' D IND. n'(K) pode ser gerado por dois elementos. Neste trabalho provaremos que todo ideal à esquerda ou à direita do anel 'E IND. n'(K) := K(('x IND. 1' ... 'x IND. n'))(' partial IND. 1, ...'partial IND. n') de operadores diferenciais sobre o corpo das séries de Laurent K(('x IND. 1', ...'x IND. n')) é gerado por dois elementos. Nós provaremos também que todo ideal à esquerda ou à direita do anel 'S IND. n -1'(K) := K(('x IND. 1', ...'X ind. n - 1"))[['x IND. n']](' partial IND. 1, ...'partial IND. n') é gerado por dois elementos e como corolário obtemos uma demonstração que todo ideal à esquerda ou à direita do anel 'D IND. 1'(K) é gerado por dois elementos. Isto está de acordo com a conjectura que diz que todo ideal à esquerda ou à direita de um anel (não comutativo) Noetheriano simples é gerado por dois elementos
Title in English
Ideals of rings of differential operators
Keywords in English
Ideals
Power series
Rings of differential operators
Stafford theorem
Weyl algebras
Abstract in English
In [12] J.T. Stafford proved that every left or right ideal of the Weyl algebra 'A IND. n'(K) = K['x IND. 1', ...'x IND. n'](' partial IND. 1, ...'partial IND. n')(K a field of characteristic zero) is generated by two elements. Consider the ring 'D IND. n' := K[['x IND. 1', ...'x IND.n']]('partial IND. 1", ...'partial IND. n) of differential operators over the ring of formal power series K[['x IND. 1', ... 'x IND. n']]: A natural question is that if every left or right ideal of 'D IND. n'(K) can be generated by two elements. In this work we will prove that every left or right ideal of the ring 'E IND. n' (K) := K(('x IND. 1', ... 'x IND. n'))('partial IND. 1,...'partial IND. n') of differential operators over the field of formal Laurent series K(('x IND. 1', ...'x IND. n'))) is generated by two elements. We will prove also that every left or right ideal of the ring 'S IND. n -1"(K) := K(('x IND. 1', ...'x IND. n'-1'))[['x IND. n]]('paertial IND. 1, ...'partial IND. n') is generated by two elements and as a corollary we obtain a proof of that every left or right ideal of the ring 'D IND. 1'(K) is generated by two elements. This is in accordance with the conjecture that says that in a (noncommutative) Noetherian simple ring, every left or right ideal is generated by two elements
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
tesedoutoradonapo.pdf (517.19 Kbytes)
Publishing Date
2011-09-01
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
CeTI-SC/STI
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2024. All rights reserved.