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Publication:
Imagen de los τ-Productos

Imagen de los τ-Productos

dc.contributor.advisor | Ortiz Albino, Reyes M. | |

dc.contributor.author | Calderón Gómez, José E. | |

dc.contributor.college | College of Arts and Sciences - Art | en_US |

dc.contributor.committee | Ocasio, Victor | |

dc.contributor.committee | Dziobiak, Stan | |

dc.contributor.department | Department of Mathematics | en_US |

dc.contributor.representative | Irizarry, Zollianne | |

dc.date.accessioned | 2019-07-01T17:47:05Z | |

dc.date.available | 2019-07-01T17:47:05Z | |

dc.date.issued | 2019-05-15 | |

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.description.graduationSemester | Spring | en_US |

dc.description.graduationYear | 2019 | en_US |

dc.identifier.uri | https://hdl.handle.net/20.500.11801/2482 | |

dc.language.iso | es | en_US |

dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |

dc.rights.holder | (c) 2019 José Emilio Calderón | en_US |

dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |

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 τ-Productos | en_US |

dc.type | Thesis | en_US |

dspace.entity.type | Publication | |

thesis.degree.discipline | Pure Mathematics | en_US |

thesis.degree.level | M.S. | en_US |

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