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Master's Dissertation
DOI
10.11606/D.55.2005.tde-03122014-163855
Document
Author
Full name
Márcio Alexandre de Oliveira Reis
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2005
Supervisor
Committee
Pérez, Victor Hugo Jorge (President)
Levcovitz, Daniel
Tomazella, João Nivaldo
Title in Portuguese
Multiplicidades e multiplicidades mistas de ideais m-primários
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Neste trabalho, estudamos as principais propriedades da teoria geral da multiplicidade algébrica de um ideal I de um anel A, com relação a um A-módulo M. A definição da multiplicidade surge a partir do conceito de comprimento e a partir disto estudamos as relações entre o símbolo da multiplicidade e o comprimento. Também estudamos a função de Hilbert associada a vários ideais M-primários e definimos as multiplicidades rnixtas, definidas originalmente por B. Teissier e J..J. Rislcr. Utilizando as propriedades da multiplicidades algébrica, calculamos o número de Milnor de algumas hipersuperfícies complexas com singularidade isolada.
Title in English
Multiplicities and mixed Multiplicites of m-primary ideals
Keywords in English
Not available
Abstract in English
In this work, wo study the main properties of general theory of algebraic multiplicities of an ideal of a ring A, with respect to A-module M. The definition of multiplicities arises out from concept of length and from this concept we study the relations among the multiplicity's symbol and the length. We also study the Hilberfs functions associated to many ideais M-primary and we define the mixed multiplicities which was defined originally by B. Teissier and J.J. Risler. Using the properties of algebraic multiplicities we calculate the Milnor's number of some complex hypersurface with isolated singularity.
 
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Publishing Date
2014-12-03
 
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