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Master's Dissertation
DOI
10.11606/D.45.2008.tde-21102010-205202
Document
Author
Full name
Heily Wagner
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2008
Supervisor
Committee
Coelho, Flavio Ulhoa (President)
Alvares, Edson Ribeiro
Braga, Clezio Aparecido
Title in Portuguese
Extensões cindidas por ideais nilpotentes
Keywords in Portuguese
dimensões homológicas
extensões cindidas
representações de álgebras
Abstract in Portuguese
Consideremos A e B duas álgebras de Artin tais que é uma extensão cindida de A pelo ideal Q, onde é um ideal nilpotente de B. Estudamos algumas propriedades homológicas das categorias modA e modB, tais como dimensão projetiva e injetiva. A partir disso mostramos que se B pertence a uma das seguintes classes: hereditária, laura, fracamente shod, shod, quase inclinada, colada à esquerda, colada à direita ou disfarçada; então A pertence a mesma classe. Além disso, restringindo nosso estudo para álgebras de dimensão finita sobre um corpo algebricamente fechado, comparamos as respectivas aljavas ordinárias, bem como suas apresentações. Finalmente, após caracterizarmos o ideal Q, exibimos alguns exemplos de extensões no contexto de álgebras de caminhos com relações, que mostram que A pode ser de uma das classes citadas sem que B o seja
Title in English
split-by-nilpotent extension
Keywords in English
algebras representation
homological dimensions
split extensions
Abstract in English
Let A and B be two Artin algebras such that B is a split-by-nilpotent extension of A by Q, were Q is a nilpotent ideal of B. We study some homological properties of the categories mod A and mod B such that the projetive and the injetive dimensions of their objects. Using this we show that if B belongs to one of this classes: hereditary, laura, weakly shod, shod, quasi-tilted, left glued, right glued or concealed; then A belongs to same class. Moreover restricting our study to finite dimensional algebras over algebraically closed fields, we compare the ordinary quivers and presentations of the corresponding algebras. Finally, after giving a characterization of ideal Q as above, we exhibit some exemples of split extensions in the context of path algebras bounded by relations, which shows that A can be one of the above cited algebras without B so
 
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DissertHeilyWagner.pdf (931.95 Kbytes)
Publishing Date
2011-05-12
 
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