论文标题
以$ ϕ $ -1的优势理想
On $ϕ$-1-Absorbing Prime Ideals
论文作者
论文摘要
在本文中，我们介绍了$ ϕ $ -1的质量理想。让$ r $为具有非零身份的通勤戒指$ 1 \ neq0 $和$ ϕ：\ Mathcal {i}（r）\ rightarrow \ Mathcal \ Mathcal {i}（r）\ cup \ cup \ airsTySet \}适当的理想$ i $ $ r $ $ r $称为$ ϕ $ -1-absorbing Prime的理想，如果对于每个nonunits $ x，y，z \ in r $ in r $ in r $，in i-ϕ（i）$，则是$ xyz \ in i $或$ xy \ in I $或$ z \ in I $ $ $。除了提供$ -1 $ -1的质量理想的许多属性和特征外，我们还确定了每个适当理想的戒指，即$ -1 $ -1-ABSORBING PRIME。
In this paper, we introduce $ϕ$-1-absorbing prime ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity $1\neq0$ and $ϕ:\mathcal{I}(R)\rightarrow\mathcal{I}(R)\cup\{\emptyset\}$ be a function where $\mathcal{I}(R)$ is the set of all ideals of $R$. A proper ideal $I$ of $R$ is called a $ϕ$-1-absorbing prime ideal if for each nonunits $x,y,z\in R$ with $xyz\in I-ϕ(I)$, then either $xy\in I$ or $z\in I$. In addition to give many properties and characterizations of $ϕ$-1-absorbing prime ideals, we also determine rings in which every proper ideal is $ϕ$-1-absorbing prime.
