Ideais Completos

• Ano de defesa: 2023
• Autor(a) principal: RIBEIRO, Ranney Ritchie Souto
• Orientador(a): LIMA, Pedro Henrique Apoliano Albuquerque
• Banca de defesa: LIMA, Pedro Henrique A. A. , MARÃO, José Antônio Pires Ferreira , PÉREZ, Victor Hugo Jorge
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Maranhão
• Programa de Pós-Graduação: PROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA/CCET
• Departamento: COORDENAÇÃO DO CURSO DE CIÊNCIA E TECNOLOGIA/CCET
• País: Brasil
• Palavras-chave em Português: ideal basicamente completo; ideal contraído; ideal completo; ideal m-completo; propriedade de Rees; ideal integralmente fechado
• Palavras-chave em Inglês: Basically full ideal; contracted ideal; full ideal; m-full ideal; Rees property; integrally closed ideal
• Área do conhecimento CNPq: Geometria Algebrica
• Link de acesso: https://tedebc.ufma.br/jspui/handle/tede/5479

The theory of integrally closed ideals in two-dimensional regular local rings (R,m) was introduced by the mathematician Oscar Ascher Zariski. Zariski’s motivation was to give algebraic meaning to the idea of complete linear systems of curves. He studied the class of the contracted ideals. It is known that contracted m-primary ideals I of R are characterized by the following property: (I : m) = (I : x) for some x ∈ m\m2. We call the ideals with this property full ideals and compare this class of ideals with the classes of m-full ideals, basically full ideals and contracted ideals in regular local rings of dimension greater than 2. The m-full ideals are easily seen as full. In this dissertation, we find a sufficient condition for a full ideal to be m-full. We also show that full, m-full, contracted, integrally closed and normal ideals are all equivalents in case of an ideal of parameter. We find a sufficient condition for a basically full parameter ideal to be full.