Imagen de los τProductos
dc.contributor.advisor  OrtizAlbino, Reyes M.  
dc.contributor.author  CalderónGómez, José E.  
dc.date.accessioned  20190701T17:47:05Z  
dc.date.available  20190701T17:47:05Z  
dc.date.issued  20190515  
dc.identifier.uri  https://hdl.handle.net/20.500.11801/2482  
dc.description.abstract  The theory of $\tau$factorizations, also known as theory of generalized factorizations, was developed by Anderson and Frazier in 2006. It was the result of a generalization of the comaximal factorizations by McAdams and Swam, replacing the condition of being comaximals to being related on the set of nonzero nonunits elements in the integral domain. Denote $D$ as an integral domain, $U(D)$ as the set of units of $D$ and $D^\#$ as the set of elements nonzero nonunits of $D$. The authors considered symmetric relations defined over the nonzero nonunits elements. The usual theory of factorizations came to be a particular case, where the relation used is $\tau=D^\#\times D^\#$. An expression of the form $a=\lambda a_1\cdot\cdot \cdot a_n$, where $\lambda\in U(D)$ and $a_i\tau a_j$ for all $1\leq i\neq j\leq n$, is called a $\tau$factorizarion of $a$. Each $a_i$ is called a $\tau$factor of $a$ and $a$ is a $\tau$product of $a_i$. Furthermore, it is possible to obtain particular cases, such as factorizations in irreducibles elements, primals, and others, by taking $\tau=S\times S$, where $S$ is the set of irreducible elements or primals respectively. This work studied the relation $\tau_R$, where $R\subseteq D\times E$, $D$ and $E$ are integral domains, and $\tau$ is defined on $D^\#$. The relation $\tau_R$ is defined as $x\tau_R y$, if and only if there exist $a,b\in D^\#$ such that $a\tau b$, $aRx$, and $bRy$. That is, $\tau_R$ is ``the image of $\tau$ with respect to the relation $R$''. The properties of $\tau_R$ that can be inherited from $\tau$ in $\tau_R$ are analyzed . It must be clarified that although the definition is given with respect to the image of a relation, most of the work is focused in different types of functions, such as one to one and surjectives functions, homomorphisms, and others. The principal objective is to provide a way to study $\tau$factorizations and structural properties using the images of the functions.  en_US 
dc.language.iso  es  en_US 
dc.rights  CC0 1.0 Universal  * 
dc.rights.uri  http://creativecommons.org/publicdomain/zero/1.0/  * 
dc.subject  factorizaciones  en_US 
dc.subject  Relaciones  en_US 
dc.subject  Dominios de integridad  en_US 
dc.subject  Función  en_US 
dc.subject  Homomorfismo  en_US 
dc.subject.lcsh  Factorization (Mathematics)  en_US 
dc.subject.lcsh  Integral domains  en_US 
dc.subject.lcsh  Functions  en_US 
dc.title  Imagen de los τProductos  en_US 
dc.type  Thesis  en_US 
dc.rights.holder  (c) 2019 José Emilio Calderón  en_US 
dc.contributor.committee  Ocasio, Victor  
dc.contributor.committee  Dziobiak, Stan  
dc.contributor.representative  Irizarry, Zollianne  
thesis.degree.level  M.S.  en_US 
thesis.degree.discipline  Pure Mathematics  en_US 
dc.contributor.college  College of Arts and Sciences  Art  en_US 
dc.contributor.department  Department of Mathematics  en_US 
dc.description.graduationSemester  Spring  en_US 
dc.description.graduationYear  2019  en_US 
Files in this item
This item appears in the following Collection(s)

Theses & Dissertations
Items included under this collection are theses, dissertations, and project reports submitted as a requirement for completing a graduate degree at UPRMayagüez.