论文标题
通勤环的半理想
Semi r-ideals of commutative rings
论文作者
论文摘要
对于具有身份的换向戒指，我们介绍和研究半$ r $ - 理想的概念，这是对$ r $ - 理想和半弹药理想的一种概括。如果每当$ a^{2} \ in I $和$ ann_ {r}（a）= 0 $，则为semutative run $ r $的理想理想$ i $称为semi $ r $ - 理想，则称为semi $ r $。确定了这类理想的几种属性和特征。特别是，我们在各种构造的背景下，例如直接产品，本地化，同构图像，理想化和合并戒指，调查了半$ r $ r $ r $ r $ r $ r $ r的。我们将半$ $ r $ - 理想的戒指扩展到半$ r $ r $ - 模块模块，并阐明其某些属性。此外，我们定义满足$ D $ ANSIHIHIHITATOR条件的子模型，并在半$ r $ -submodules时证明它们是合理的。
For commutative rings with identity, we introduce and study the concept of semi $r$-ideals which is a kind of generalization of both $r$-ideals and semiprime ideals. A proper ideal $I$ of a commutative ring $R$ is called semi $r$-ideal if whenever $a^{2}\in I$ and $Ann_{R}(a)=0$, then $a\in I$. Several properties and characterizations of this class of ideals are determined. In particular, we investigate semi $r$-ideal under various contexts of constructions such as direct products, localizations, homomorphic images, idealizations and amalagamations rings. We extend semi $r$-ideals of rings to semi $r$-submodules of modules and clarify some of their properties. Moreover, we define submodules satisfying the $D$-annihilator condition and justify when they are semi $r$-submodules.
