论文标题
通勤环的R理想的概括
Generalizations of r-ideals of commutative rings
论文作者
论文摘要
在这项研究中，我们介绍了$ r $ $ - 理想的概念在具有非零身份的交换环中的概念。让$ r $为$ 0 \ neq1 $，$ l（r）$的换向戒指，为$ r $的所有理想的晶格。假设$ ϕ：l（r）\ rightarrow l（r）\ cup \ left \ {\ emptySet \ right \} $是一个函数。适当的理想$ i $ $ r $ $ r $称为$ ϕ-r $ - $ r $，如果每当$ ab \ in in $ a $和$ ann（a）=（a）=（0）$的$ a $ r $ $ r $，则意味着每个$ a，b \ in in i $ in R in r。
In this study, we present the generalization of the concept of $r$-ideals in commutative rings with nonzero identity. Let $R$ be a commutative ring with $0\neq1$ and $L(R)$ be the lattice of all ideals of $R$. Suppose that $ϕ:L(R)\rightarrow L(R)\cup\left\{\emptyset\right\}$ is a function. A proper ideal $I$ of $R$ is called a $ϕ-r$-ideal of $R$ if whenever $ab\in I$ and $Ann(a)=(0)$ imply that $b\in I$ for each $a,b\in R.$ In addition to giving many properties of $ϕ-r$-ideal, we also examine the concept of $ϕ-r$-ideal in trivial ring extension and use them to characterize total quotient rings.
