论文标题
2-吸收的准主要理想的概括
Generalization of 2-absorbing quasi primary ideals
论文作者
论文摘要
在本文中，我们介绍并研究了$ -2 $ -2 $ -2的准主要理想的概念。令$ r $为具有非零身份的交换戒指，而$ l（r）$是$ 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 $ a $ r $称为$ ϕ $ -2-absorbing $ r $ IF $ a，b，c \ in r $ in r $ in r $ in r $ in r $ in i-ϕ（i），$ in i-ϕ（i），然后是$ abc \ in \ sqrt {i} $或$ ac \ in \ in \ in \ in \ in \ sqrt或$ bc \ in \ sqrt {i} $。除了提供$ -2 $ -2的准主要理想的许多属性外，我们还使用它们来表征von Neumann常规环。
In this article, we introduce and study the concept of $ϕ$-2-absorbing quasi primary ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity 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 $ϕ$-2-absorbing quasiprimary ideal of $R$ if $a,b,c\in R$ and whenever $abc\in I-ϕ(I),$ then either $ab\in\sqrt{I}$ or $ac\in\sqrt{I}$ or $bc\in\sqrt{I}$. In addition to giving many properties of $ϕ$-2-absorbing quasi primary ideals, we also use them to characterize von Neumann regular rings.
