On Weakly 1-Absorbing Prime Ideals

Abstract

This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $A$ be a commutative ring with a nonzero identity $1\ne 0$. 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 $0\ne xyz\in P$, 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.

14 pages, original research paper