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 every nonunits \(x,y,z\in A\ \)with \(0\ne xyz\in P,\ \)then \(xy\in P\) 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 \(X.\ \)

本文介绍并研究了交换环中的弱1吸收素理想。让\（A \ \）是具有非零身份交换环\（1 \ 0 NE \）一个适当的理想\（P \ \）的\（A \ \）被说成是一种弱1吸收素如果对每个非单位\（x \ y，z \ in A \ \）带有\（0 \ ne xyz \ in P，\ \）则\（xy \ in P \）或\（z \ in P. \ \）除了给出弱吸收1素数理想的许多性质和特征外，我们还确定了每个合适的理想都是弱吸收1素数的环。此外，我们研究了C（X），它是拓扑空间\（X. \ \）的连续函数的环