Composición de relaciones y $τ$ -factorizaciones
Composición de relaciones y $τ$-factorizaciones
摘要：
整环上的$τ$ -因子分解理论是由Anderson和Frazier发展起来的。这个理论描述了所有已知的因式分解，并为创造新的因式分解提供了机会。它可以被看作是一个限制结构的乘法运算，通过考虑一个对称关系$τ$的非零非单位元素的集合上的整环。这项工作的主要目标是研究的$τ$ -因子分解的概念，当$τ$是一个组合的两个或多个关系。为了实现这一点，可以从给定的关系得到的具体性质进行了验证和分析。一些研究的性质是最有名的包括：自反性，对称性，传递性，反对称性。以及其他与$τ$ -因子分解理论相关的关系，如：除关系、保伴关系和乘关系。
英文摘要：
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.
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