论文标题
有限和有限分数域
Bounded and finite factorization domains
论文作者
论文摘要
如果每个非零非单位因素都陷入不缩合，则整体域是原子质。令$ r $为一个不可或缺的域。 We say that $R$ is a bounded factorization domain if it is atomic and for every nonzero nonunit $x \in R$, there is a positive integer $N$ such that for any factorization $x = a_1 \cdots a_n$ of $x$ into irreducibles $a_1, \dots, a_n$ in $R$, the inequality $n \le N$ holds.此外，我们说$ r $是一个有限的分解域，如果它是原子化域，而每一个非零的nonunit中的$ r $ raunit in $ r $ castion in Indreducibles中仅以有限的方式（最终订购和同事）。 D. D. Anderson，D。F。Anderson和M. Zafrullah在原子整合域中的分解研究中引入了有限和有限分解域的概念。在这里，我们对有限和有限分解域的一些最相关的结果进行了调查。
An integral domain is atomic if every nonzero nonunit factors into irreducibles. Let $R$ be an integral domain. We say that $R$ is a bounded factorization domain if it is atomic and for every nonzero nonunit $x \in R$, there is a positive integer $N$ such that for any factorization $x = a_1 \cdots a_n$ of $x$ into irreducibles $a_1, \dots, a_n$ in $R$, the inequality $n \le N$ holds. In addition, we say that $R$ is a finite factorization domain if it is atomic and every nonzero nonunit in $R$ factors into irreducibles in only finitely many ways (up to order and associates). The notions of bounded and finite factorization domains were introduced by D. D. Anderson, D. F. Anderson, and M. Zafrullah in their systematic study of factorization in atomic integral domains. Here we provide a survey of some of the most relevant results on bounded and finite factorization domains.
