论文标题
在多项式半分的算术上
On the arithmetic of polynomial semidomains
论文作者
论文摘要
只要对$（s，+）$和$（s，\ cdot）$，一个积分域$ r $的子集$ s $称为半域。 Anderson，Anderson和Zafrullah于1990年启动了整体域中的因素化研究，此后对该领域进行了系统的研究。在本文中，我们研究了半个构构族更一般环境中因素化的分裂性和算术。我们特别关注从半构域到其（laurent）多项式半分的最标准的分解性和分解特性的提升。与积分域一样，在这里，我们证明满足链条条件在主理想上，具有有限的因素化以及在半分等级中的有限因素化上升的特性。我们还考虑了原子的属性和具有独特分解的特性（通常都没有上升）。在整篇文章中，我们提供了几个旨在阐明半分因算术的示例。
A subset $S$ of an integral domain $R$ is called a semidomain provided that the pairs $(S,+)$ and $(S, \cdot)$ are semigroups with identities. The study of factorizations in integral domains was initiated by Anderson, Anderson, and Zafrullah in 1990, and this area has been systematically investigated since then. In this paper, we study the divisibility and arithmetic of factorizations in the more general context of semidomains. We are specially concerned with the ascent of the most standard divisibility and factorization properties from a semidomain to its semidomain of (Laurent) polynomials. As in the case of integral domains, here we prove that the properties of satisfying the ascending chain condition on principal ideals, having bounded factorizations, and having finite factorizations ascend in the class of semidomains. We also consider the ascent of the property of being atomic and that of having unique factorization (none of them ascends in general). Throughout the paper we provide several examples aiming to shed some light upon the arithmetic of factorizations of semidomains.
