论文标题
关于弱的1次理想
On Weakly 1-Absorbing Prime Ideals
论文作者
论文摘要
本文介绍并研究了弱点1的弱点理想。令$ a $为具有非零身份$ 1 \ neq 0 $的交换戒指。如果每个nonunits $ x，y，z \ in P $ $ x，y，z \，则适当的理想$ p $ $ a $ a $是一个弱的1个质量理想，如果$ x，y，z \ in P $ $ 0 \ neq xyz \，则在p $中$ xy \ in p $或$ z \。除了提供许多属性和弱吸收质量理想的属性和表征外，我们还确定每个适当理想的环节都是弱的1-源。此外，我们在$ c（x）$中研究了弱点的质量理想，这是拓扑空间x的连续功能的环。
This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $A$ be a commutative ring with a nonzero identity $1\neq 0$. A proper ideal $P$ of $A$ is said to be a weakly 1-absorbing prime ideal if for each nonunits $x, y, z \in A$ with $0\neq xyz \in P$, then either $xy \in P$ or $z \in P$. In addition to give many properties and characterizations of weakly 1-absorbing prime ideals, we also determine rings in which every proper ideal is weakly 1-absorbing prime. Furthermore, we investigate weakly 1-absorbing prime ideals in $C(X)$, which is the ring of continuous functions of a topological space X.
