Idealizadores tangenciais e derivações de Anéis de Stanley-Reisner

• Ano de defesa: 2012
• Autor(a) principal: Oliveira, Ana Karine Rodrigues de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraí­ba; BR; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Derivação; Idealizador tangencial; Ideal diagonal; Zariski-Lipman; Anéis de Stanley-Reisner; Derivation; Tangential idealizer; Optimal diagonal; Rings Stanley-Reisner; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/7365

The present dissertation furnishes a detailed study about modules of logarithmic derivations, here dubbed tangential idealizers, and some of their main features. Initially, several comparisons between such modules are investigated starting from sufficiently related ideals, motivated by a previous study due to Kaplansky as well as by their close relationship with the classical theory of differential ideals of Seidenberg. We then obtain the first central result, which describes a primary decomposition of the tangential idealizer of an ideal without embedded primary component. Finally, in the second main result, we explore the structure of the derivation module for the class of Stanley-Reisner rings, thus corresponding to tangential idealizers of monomial ideals. An application of such a result is an affirmative answer for the homological Zariski-Lipman conjecture for the present class of rings.