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dc.contributor.advisorCastellini, Gabriele
dc.contributor.authorLópez-Gerena, Juan O.
dc.description.abstractIn the category of abelian groups, there exists a relationship between torsion theories and idempotent radicals where we can use one to find the other. In the process we can learn of different properties that apply to the associated subclasses. We can also use a pre-radical to obtain a closure operator and a closure operator to obtain a pre-radical. The properties of the pre-radical (whether it’s idempotent or a radical) indicate corresponding properties of the closure operator and vice-versa. In this thesis, we determine how much of the relationship that exists between closure operators, torsion theories and radicals in the category of abelian groups (Ab) can be extended to the category of all groups (Grp). Once it’s clear which properties do not apply, our goal is to find, for each property, which modifications can be made so that the property still holds.
dc.description.abstractEn la categoría de grupos abelianos, existe una relación entre las teorías de torsión y los radicales idempotentes donde podemos usar uno para encontrar el otro. En el proceso podemos aprender sobre diferentes propiedades que aplican a las subclases implicadas. Además, podemos usar un pre-radical para obtener un operador de clausura y un operador de clausura para obtener un pre-radical. Las propiedades del pre-radical (si es idempotente o un radical) nos indican propiedades correspondientes en el operador de clausura y vice-versa. En esta tesis determinamos qué aspectos de la relación que existe entre los operadores de clausura, teorías de torsión y radicales en la categoría de grupos abelianos (Ab) se pueden extender a la categoría de todos los grupos (Grp). Una vez tengamos claro cuales propiedades no aplican, nuestra meta es investigar, para cada propiedad, qué modificaciones se les puede hacer para que la propiedad todavía aplique.
dc.subjectAbelian groupsen_US
dc.subjectTorsion theoriesen_US
dc.subjectClosure operatorsen_US
dc.subject.lcshClosure operatorsen_US
dc.subject.lcshTorsion theory (Algebra)en_US
dc.subject.lcshNon-Abelian groupsen_US
dc.titleClosure operators, torsion theories, and radicals in a non-abelian environmenten_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c)2009 Juan O López Gerenaen_US
dc.contributor.committeeWalker Ramos, Uroyoán
dc.contributor.committeeDziobiak, Wieslaw
dc.contributor.representativeCastellanos, Dorial Mathematicsen_US
dc.contributor.collegeCollege of Arts and Sciences - Sciencesen_US
dc.contributor.departmentDepartment of Mathematicsen_US

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    Items included under this collection are theses, dissertations, and project reports submitted as a requirement for completing a graduate degree at UPR-Mayagüez.

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