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Master's Dissertation
DOI
10.11606/D.45.2012.tde-27012014-172156
Document
Author
Full name
Helen Samara dos Santos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Milies, Francisco Cesar Polcino (President)
Ferraz, Raul Antonio
Paques, Antonio
Title in Portuguese
Injetividade e Módulos Pobres
Keywords in Portuguese
módulo injetivo
módulo pobre
teoria de anéis
Abstract in Portuguese
O objetivo deste trabalho é estudar algumas classes de anéis. Para isso, introduzimos o conceito de módulo pobre e provamos algumas propriedades básicas destes módulos. Além disso, estudamos quais hipóteses sobre um anel R fazem com que alguma família da classe dos R-módulos seja uma família destituída (famílias tais que todo R-módulo é pobre), uma família sem classe média (famílias tais que todo R-módulo ou é pobre ou é injetivo) ou uma família que é uma utopia (famílias tais que todo R-módulo não é pobre).
Title in English
Injectivity and Poor Modules
Keywords in English
injective module
poor module
ring theory
Abstract in English
The goal of this dissertation is to study certain classes of rings. To this end, we introduce the definition of a poor module and prove some basic properties of these modules. Furthermore, we study which hypotheses on a ring R turn some classes of R-modules into a destitute family (families such that every R-module is poor), a family with no middle class (families such that every R-module is either poor or injective) or a family that is an utopia (families such that every R-module is not poor)
 
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Publishing Date
2014-03-25
 
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