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Master's Dissertation
DOI
Document
Author
Full name
Matheus Koveroff Bellini
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Tomita, Artur Hideyuki (President)
Aurichi, Leandro Fiorini
Pestov, Vladimir
Title in Portuguese
Álgebra de semigrupo na compactificação de Stone-Cech de semigrupos discretos
Keywords in Portuguese
Álgebra na compactificação
Álgebra topológica
Topologia geral
Abstract in Portuguese
Dado um semigrupo S e a topologia discreta sobre ele, é possível estender a operação ao compactificado de Stone-Cech beta(S) de forma que seja contínua à direita. Diversas propriedades algébricas tais como cancelatividade, comutatividade e ser grupo implicam em propriedades algébrico-topológicas de beta(S). Em particular, o conjunto dos naturais com a soma e/ou o produto é o mais explorado: resultados tais como a existência de 2^c ideais á esquerda minimais e de cadeias decrescentes de idempotentes são mostrados e suas consequências discutidas.
Title in English
Semigroup algebra in the Stone-Cech compactification of discrete semigroups
Keywords in English
Algebra in the compactification
General topology
Topological algebra
Abstract in English
Given a semigroup S and its discrete topology, it is possible to extend its operation to its Stone-Cech compactification beta(S) so that it is right-continuous. Several algebraic properties such as cancellativity, commutativity annd being a group influence topological-algebraic properties of beta(S). Most especially, the set of natural numbers with addition and/or multiplication is explored: results such as the existence of 2^c minimal left ideals or of decreasing chains of idempotents are shown and their consequences analysed.
 
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Publishing Date
2019-05-29
 
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