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dc.contributor.advisorCastellini, Gabriele
dc.contributor.authorCoronel-Suárez, Angy C.
dc.description.abstractIn 1971, Joachim Lambek published a result which gives an equivalence between torsion theo- ries (B,C) and idempotent radicals T in the category Mod R, establishing some properties of the classes of R-modules B and C and performing a characterization of these classes using the radical T. Recently, D. Dikranjan, W. Tholen and G. Castellini have defined, in this category, new closure operators based on pre-radicals and reciprocally, they have defined radicals based on closure operators. In this thesis we have made some modifications to these results, defining new concepts and finding some conditions to be satisfied by the classes B and C in order to establish some conection between torsion theories and radicals in the category Rng. We have also defined closure operators using pre-radicals and vice versa, establishing a non bijective correspon- dence between these two concepts in this category.
dc.description.abstractEn 1971, Joachim Lambek publicó un resultado que da una equivalencia entre las teorías de torsión (B, C) y los radicales idempotentes T en la categoría Mod R, estableciendo algunas propiedades que cumplen las clases de R-módulos B y C y realizando una caracterización de éstas clases usando el radical T. Recientemente, D. Dikranjan, W. Tholen y G. Castellini han definido, en esta misma categoría, nuevos operadores de clausura basados en pre-radicales y recíprocamente, han definido radicales basados en operadores de clausura. En esta tesis hemos realizado algunas modificaciones a estos resultados, definiendo nuevos conceptos y encontrando algunas condiciones que deben cumplir las clases B y C para así poder establecer alguna relacionan entre las teorías de torsión y los radicales en la categoría Rng. Igualmente, hemos construido operadores de clausura usando pre-radicales y viceversa, estableciendo una correspondencia no biyectiva entre estos dos conceptos en esta categoría.
dc.subjectTorsion theoriesen_US
dc.subjectRadical Ten_US
dc.subjectClosure operatorsen_US
dc.subject.lcshTorsion theory (Algebra)en_US
dc.subject.lcshClosure operatorsen_US
dc.subject.lcshRings (Algebra)en_US
dc.titleTorsion theories, radicals and closure operators in the category of ringsen_US
dc.title.alternativeTeorias de torsión, radicales y operadores de clausura en la categoría de anillosen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c)2009 Angy C. Coronel Suárezen_US
dc.contributor.committeeCáceres, Luis F.
dc.contributor.committeeWalker, Uroyoán
dc.contributor.representativePalomera, Rogelio 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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