  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.
