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Doctoral Thesis
DOI
10.11606/T.55.2010.tde-21052010-100742
Document
Author
Full name
Marcela Duarte da Silva
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2010
Supervisor
Committee
Pérez, Victor Hugo Jorge (President)
Bedregal, Roberto Callejas
Brumatti, Paulo Roberto
Hernandes, Marcelo Escudeiro
Levcovitz, Daniel
Title in Portuguese
Módulos coeficientes em álgebras
Keywords in Portuguese
Módulo de Ratliff-Rush
Módulos coeficientes
Multiplicidade de Buchsbaum-Rim
Polinômio de Buchsbaum-Rim
Abstract in Portuguese
Em 1991, Kishor Shah definiu e estudou os ideais coeficientes 'I IND. {k}' , para todo inteiro k = 0, . . . , d, associados a um ideal m-primário I de um anel Noetheriano local d-dimensional, (R,m). Esses ideais, 'I IND. {k} ' , são os maiores ideais de R que contem o ideal I tais que os primeiros k + 1 coeficientes dos polinômios de Hilbert-Samuel de I e 'I IND. {k} ' coincidem. O resultado principal do trabalho de Kishor Shah é provar teoremas de estrutura para estes ideais. Na sua Tese de Doutorado, Jung-Chen Liu generalizou alguns aspectos do trabalho de Kishor Shah para R-submódulos E de 'R POT. p', definindo os submódulos coeficientes 'E IND. {k}' , para k = 0, . . . , d + p 1. Por´em Jung-Chen Liu não provou o teorema de estrutura para tais módulos coeficientes. Neste trabalho, estenderemos os trabalhos de Kishor Shah e de Jung-Chen Liu para R-submódulos E 'ESTÁ CONTIDO EM' F de 'R POT. p', onde 'ell IND. R' ('F SOBRE E' ) < 'INFINITO', definindo os módulos coeficientes 'E POT F IND. {k}', para todo inteiro k = 0, . . . , d + p 1 e provando o teorema de estrutura para tais módulos
Title in English
Coefficient modules in algebras
Keywords in English
Buchsbaum-Rim multiplicity
Buchsbaum-Rim multipliity
Buchsbaum-Rim polynomial
Ratliff-Rush module and coefficient modules
Abstract in English
In 1991, Kishor Shah defined and studied coeficient ideals 'I ind {k}. ' , for integers k = 0, . . . , d, associated to an ideal m-primary I of a Noetherian local ring of dimension, (R,m). This ideals, 'I ind {k}'. , are the biggest ideals of R that contains the ideal I such that the first k+1 Hilbert-Samuel coefficients of I and 'I IND. {k}' are igual. The main result of Kishor Shahs work is to prove the struture theorem of such ideals. In his P.h.D thesis, Jung-Chen Liu generalized some aspects of Kishor Shahs work in the case of R-submodules E of 'R POT. p', defining the coefficients submodules 'E IND. {k}, ' for integers k = 0, . . . , d+p1. But Jung-Chen Liu didnt prove the struture theorem for such coefficients modules. In this work, we extended the works of Kishor Shah and of Jung-Chen Liu for R-submodules E 'ARE THIS CONTAINED' F of 'R POT. p', where 'ell IND. R ('F ON E' ) < 'THE INFINITE' , defining the coefficients modules 'E POT. F IND. {k}', for integers k = 0, . . . , d + p 1 and proving the struture theorem for such modules
 
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Publishing Date
2010-05-24
 
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