arXiv subjects
Publications and source records attributed to David Fernando Méndez Oyuela.
This paper analyzes a possible link between Category Theory and Generalized Factorization Theory developed by Anderson and Frazier. Specifically in the context of what has been worked on in previous works, where compositions of relations and their link with $τ$-factorizations are analyzed.
The theory of $τ$-factorizations on integral domains was developed by Anderson and Frazier. This theory characterized all the known factorizations and opened the opportunity to create new ones. It can be visualized as a restriction to the structure's multiplicative operation, by considering a symmetric relation $τ$ on the set of non-zero non-unit elements of an integral domain. The main goal of this work is to study the $τ$-factorization concept, when $τ$ is a composition of two or more relations. To achieve this, the specific properties one can obtain from the given relations are verified and analyzed. Some of the studied properties which are the most known include: reflexivity, symmetry, transitivity, antisymmetry. And others related to the $τ$-factorization theory, like: divisive, associate-preserving and multiplicative relations.