论文标题
以一口气分解的换向环
Commutative rings with one-absorbing factorization
论文作者
论文摘要
令$ r $为具有非零身份的交换戒指。 A. Yassine等。在论文（Yassine，Nikmehr和Nikandish，2020年）中定义的，$ 1 $的概念概念以下内容如下：一个适当的理想理想$ i $ $ r $的$ 1 $ -sbsorbing Prime prime prime prime prime prime pripe prime nover y in I $ xyz \ in I $ xyz \ in I n“ I in I $ xy in in I ni“ y in i ni“ y y in i”我$。我们使用$ 1 $ - 吸收质量的理想的概念来研究那些适当的理想的循环，其中每个适当的理想都是$ 1 $ - 吸收的主要理想的产品（我们称它们为$ oaf $ rings）。任何$ oaf $ ring最多都有一个尺寸，而本地$ oaf $ domains $（d，m）$都是原子，使得$ m^2 $是通用的。
Let $R$ be a commutative ring with nonzero identity. A. Yassine et al. defined in the paper (Yassine, Nikmehr and Nikandish, 2020), the concept of $1$-absorbing prime ideals as follows: a proper ideal $I$ of $R$ is said to be a $1$-absorbing prime ideal if whenever $xyz\in I$ for some nonunit elements $x,y,z\in R$, then either $xy\in I$ or $z\in\ I$. We use the concept of $1$-absorbing prime ideals to study those commutative rings in which every proper ideal is a product of $1$-absorbing prime ideals (we call them $OAF$-rings). Any $OAF$-ring has dimension at most one and local $OAF$-domains $(D,M)$ are atomic such that $M^2$ is universal.
